L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

C\u00e1c c\u00e2u \u1edf b\u00ean tr\u00e1i l\u00e0 c\u00e1c c\u00e2u kh\u1eb3ng \u0111\u1ecbnh, c\u00f3 t\u00ednh \u0111\u00fang sai<\/p>\n\n\n\n

C\u00e1c c\u00e2u \u1edf b\u00ean ph\u1ea3i kh\u00f4ng th\u1ec3 n\u00f3i l\u00e0 \u0111\u00fang hay sai<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 4<\/strong>: N\u00eau v\u00ed d\u1ee5 v\u1ec1 nh\u1eefng c\u00e2u l\u00e0 m\u1ec7nh \u0111\u1ec1 v\u00e0 nh\u1eefng c\u00e2u kh\u00f4ng l\u00e0 m\u1ec7nh \u0111\u1ec1.<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

VD v\u1ec1 c\u00e2u l\u00e0 m\u1ec7nh \u0111\u1ec1:<\/p>\n\n\n\n

5 l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1 <\/p>\n\n\n\n

S\u1eaft l\u00e0 kim lo\u1ea1i.<\/p>\n\n\n\n

VD v\u1ec1 c\u00e2u kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ec7nh \u0111\u1ec1:<\/p>\n\n\n\n

H\u00f4m nay l\u00e0 th\u1ee9 m\u1ea5y?<\/p>\n\n\n\n

Tr\u1eddi \u0111\u1eb9p qu\u00e1!<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 5<\/strong>: X\u00e9t c\u00e2u \u201cx > 3\u201d. H\u00e3y t\u00ecm hai gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a x \u0111\u1ec3 t\u1eeb c\u00e2u \u0111\u00e3 cho, nh\u1eadn \u0111\u01b0\u1ee3c m\u1ed9t m\u1ec7nh \u0111\u1ec1 \u0111\u00fang v\u00e0 m\u1ed9t m\u1ec7nh \u0111\u1ec1 sai.<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/ins><\/p>\n\n\n\n

V\u1edbi x = 5, m\u1ec7nh \u0111\u1ec1 nh\u1eadn \u0111\u01b0\u1ee3c l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u00fang<\/p>\n\n\n\n

V\u1edbi x =1, m\u1ec7nh \u0111\u1ec1 nh\u1eadn \u0111\u01b0\u1ee3c l\u00e0 m\u1ec7nh \u0111\u1ec1 sai<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 6<\/strong>: H\u00e3y ph\u1ee7 \u0111\u1ecbnh c\u00e1c m\u1ec7nh \u0111\u1ec1 sau:<\/ins><\/p>\n\n\n\n

P: \u201c \u03c0 l\u00e0 m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9\u201d;<\/p>\n\n\n\n

Q: \u201cT\u1ed5ng hai c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c l\u1edbn h\u01a1n c\u1ea1nh th\u1ee9 ba\u201d.<\/p>\n\n\n\n

X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 tr\u00ean v\u00e0 m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a ch\u00fang.<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a P: P\u2212<\/em> \u201c \u03c0 kh\u00f4ng l\u00e0 m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9\u201d. <\/p>\n\n\n\n

P l\u00e0 m\u1ec7nh \u0111\u1ec1 sai, P\u2212<\/em> l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u00fang. <\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a Q: Q\u2212<\/em> \u201cT\u1ed5ng hai c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng c\u1ea1nh th\u1ee9 ba\u201d.<\/p>\n\n\n\n

Q l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u00fang, Q\u2212<\/em> l\u00e0 m\u1ec7nh \u0111\u1ec1 sai. <\/ins><\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 6<\/strong>: T\u1eeb c\u00e1c m\u1ec7nh \u0111\u1ec1:<\/p>\n\n\n\n

P: \u201cGi\u00f3 m\u00f9a \u0110\u00f4ng B\u1eafc v\u1ec1\u201d<\/p>\n\n\n\n

Q: \u201cTr\u1eddi tr\u1edf l\u1ea1nh\u201d<\/p>\n\n\n\n

H\u00e3y ph\u00e1t bi\u1ec3u m\u1ec7nh \u0111\u1ec1 P \u21d2 Q<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

P \u21d2 Q: \u201c n\u1ebfu gi\u00f3 m\u00f9a \u0110\u00f4ng B\u1eafc v\u1ec1 th\u00ec tr\u1eddi tr\u1edf l\u1ea1nh.\u201d<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 7<\/strong>: Cho tam gi\u00e1c ABC. T\u1eeb c\u00e1c m\u1ec7nh \u0111\u1ec1 <\/p>\n\n\n\n

P: \u201cTam gi\u00e1c ABC c\u00f3 hai g\u00f3c b\u1eb1ng 60^{o<\/sup> \u201d<\/p>\n\n\n\n}

Q: \u201cABC l\u00e0 m\u1ed9t tam gi\u00e1c \u0111\u1ec1u\u201d<\/p>\n\n\n\n

H\u00e3y ph\u00e1t bi\u1ec3u \u0111\u1ecbnh l\u00ed P \u21d2 Q. N\u00eau gi\u1ea3 thi\u1ebft, k\u1ebft lu\u1eadn v\u00e0 ph\u00e1t bi\u1ec3u l\u1ea1i \u0111\u1ecbnh l\u00ed n\u00e0y d\u01b0\u1edbi d\u1ea1ng \u0111i\u1ec1u ki\u1ec7n c\u1ea7n, \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7.<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

P \u21d2 Q: \u201c N\u1ebfu tam gi\u00e1c ABC c\u00f3 hai g\u00f3c b\u1eb1ng 60^{o<\/sup> th\u00ec ABC l\u00e0 m\u1ed9t tam gi\u00e1c \u0111\u1ec1u\u201d<\/p>\n\n\n\n}

Gi\u1ea3 thi\u1ebft: \u201cTam gi\u00e1c ABC c\u00f3 hai g\u00f3c b\u1eb1ng 60^{o<\/sup> \u201d<\/p>\n\n\n\n}

K\u1ebft lu\u1eadn: \u201cABC l\u00e0 m\u1ed9t tam gi\u00e1c \u0111\u1ec1u\u201d<\/p>\n\n\n\n

Ph\u00e1t bi\u1ec3u l\u1ea1i \u0111\u1ecbnh l\u00ed n\u00e0y d\u01b0\u1edbi d\u1ea1ng \u0111i\u1ec1u ki\u1ec7n c\u1ea7n: \u201cABC l\u00e0 m\u1ed9t tam gi\u00e1c \u0111\u1ec1u l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 tam gi\u00e1c ABC c\u00f3 hai g\u00f3c b\u1eb1ng 60^{o<\/sup>\u201d<\/p>\n\n\n\n}

Ph\u00e1t bi\u1ec3u l\u1ea1i \u0111\u1ecbnh l\u00ed n\u00e0y d\u01b0\u1edbi d\u1ea1ng \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 : \u201cTam gi\u00e1c ABC c\u00f3 hai g\u00f3c b\u1eb1ng 60^{o<\/sup> l\u00e0 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 \u0111\u1ec3 ABC l\u00e0 tam gi\u00e1c \u0111\u1ec1u\u201d<\/p>\n\n\n\n}

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 7<\/strong>: Cho tam gi\u00e1c ABC. X\u00e9t c\u00e1c m\u1ec7nh \u0111\u1ec1 d\u1ea1ng P \u21d2 Q sau<\/p>\n\n\n\n

a)N\u1ebfu ABC l\u00e0 m\u1ed9t tam gi\u00e1c \u0111\u1ec1u th\u00ec ABC l\u00e0 m\u1ed9t tam gi\u00e1c c\u00e2n.<\/p>\n\n\n\n

b)N\u1ebfu ABC l\u00e0 m\u1ed9t tam gi\u00e1c \u0111\u1ec1u th\u00ec ABC l\u00e0 m\u1ed9t tam gi\u00e1c c\u00e2n v\u00e0 c\u00f3 m\u1ed9t g\u00f3c b\u1eb1ng 60^{o<\/sup><\/p>\n\n\n\n}

H\u00e3y ph\u00e1t bi\u1ec3u c\u00e1c m\u1ec7nh \u0111\u1ec1 Q \u21d2 P t\u01b0\u01a1ng \u1ee9ng v\u00e0 x\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a ch\u00fang.<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

a) N\u1ebfu ABC l\u00e0 m\u1ed9t tam gi\u00e1c c\u00e2n th\u00ec ABC l\u00e0 tam gi\u00e1c \u0111\u1ec1u<\/p>\n\n\n\n

\u0110\u00e2y l\u00e0 m\u1ec7nh \u0111\u1ec1 sai<\/p>\n\n\n\n

b) N\u1ebfu ABC l\u00e0 m\u1ed9t tam gi\u00e1c c\u00e2n v\u00e0 c\u00f3 m\u1ed9t g\u00f3c b\u1eb1ng 60^{o<\/sup> th\u00ec ABC l\u00e0 m\u1ed9t tam gi\u00e1c \u0111\u1ec1u<\/p>\n\n\n\n}

\u0110\u00e2y l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u00fang<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 8<\/strong>: Ph\u00e1t bi\u1ec3u th\u00e0nh l\u1eddi m\u1ec7nh \u0111\u1ec1 sau:<\/ins><\/p>\n\n\n\n

\u2200n \u2208 Z : n + 1 > n <\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1 n\u00e0y \u0111\u00fang hay sai ?<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

V\u1edbi m\u1ecdi n thu\u1ed9c t\u1eadp s\u1ed1 nguy\u00ean, n + 1 l\u1edbn h\u01a1n n <\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1 n\u00e0y \u0111\u00fang<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 8<\/strong>: Ph\u00e1t bi\u1ec3u th\u00e0nh l\u1eddi m\u1ec7nh \u0111\u1ec1 sau:<\/p>\n\n\n\n

\u2203 x \u2208 Z : x^{2<\/sup> = x<\/p>\n\n\n\n}

M\u1ec7nh \u0111\u1ec1 n\u00e0y \u0111\u00fang hay sai ?<\/ins><\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

T\u1ed3n t\u1ea1i s\u1ed1 nguy\u00ean m\u00e0 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a n\u00f3 b\u1eb1ng ch\u00ednh n\u00f3. <\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1 n\u00e0y \u0111\u00fang v\u00ec 0 \u2208 Z; 0^{2<\/sup> = 0, 12<\/sup> = 1. <\/p>\n\n\n\n}

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 8<\/strong>: H\u00e3y ph\u00e1t bi\u1ec3u m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a m\u1ec7nh \u0111\u1ec1 sau<\/p>\n\n\n\n

P: \u201cM\u1ecdi \u0111\u1ed9ng v\u1eadt \u0111\u1ec1u di chuy\u1ec3n \u0111\u01b0\u1ee3c\u201d.<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

\u201cT\u1ed3n t\u1ea1i \u0111\u1ed9ng v\u1eadt kh\u00f4ng di chuy\u1ec3n \u0111\u01b0\u1ee3c\u201d<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 9<\/strong>: H\u00e3y ph\u00e1t bi\u1ec3u m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a m\u1ec7nh \u0111\u1ec1 sau<\/ins><\/p>\n\n\n\n

P: \u201cC\u00f3 m\u1ed9t h\u1ecdc sinh c\u1ee7a l\u1edbp kh\u00f4ng th\u00edch h\u1ecdc m\u00f4n To\u00e1n\u201d.<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n\n\n\n

\u201cT\u1ea5t c\u1ea3 h\u1ecdc sinh c\u1ee7a l\u1edbp \u0111\u1ec1u th\u00edch h\u1ecdc m\u00f4n To\u00e1n\u201d<\/p>\n\n\n\n

B\u00e0i 1 (trang 9 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> Trong c\u00e1c c\u00e2u sau, c\u00e2u n\u00e0o l\u00e0 m\u1ec7nh \u0111\u1ec1, c\u00e2u n\u00e0o l\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn?<\/p>\n\n\n\n

a) 3 + 2 = 7 ; \t        b) 4 + x = 3;<\/p>\n\n\n\n

c) x + y > 1 ;\t        d) 2 – \u221a5 < 0<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/ins><\/p>\n\n\n\n

a) 3 + 2 = 7 l\u00e0 m\u1ec7nh \u0111\u1ec1 v\u00e0 l\u00e0 m\u1ec7nh \u0111\u1ec1 sai<\/p>\n\n\n\n

V\u00ec 3 + 2 = 5 \u2260 7<\/p>\n\n\n\n

b) 4 + x = 3 l\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn<\/p>\n\n\n\n

V\u00ec v\u1edbi m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a x ta \u0111\u01b0\u1ee3c m\u1ed9t m\u1ec7nh \u0111\u1ec1.<\/p>\n\n\n\n

V\u00ed d\u1ee5 : v\u1edbi x = 1 ta c\u00f3 m\u1ec7nh \u0111\u1ec1 \u00ab 4 + 1 = 3 \u00bb. <\/p>\n\n\n\n

v\u1edbi x = \u20131 ta c\u00f3 m\u1ec7nh \u0111\u1ec1 \u00ab 4 + (\u20131) = 3 \u00bb. <\/p>\n\n\n\n

v\u1edbi x = 0 ta c\u00f3 m\u1ec7nh \u0111\u1ec1 4 + 0 = 3. <\/p>\n\n\n\n

c) x + y > 1 l\u00e0 m\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn<\/p>\n\n\n\n

V\u00ec v\u1edbi m\u1ed7i c\u1eb7p gi\u00e1 tr\u1ecb c\u1ee7a x, y ta \u0111\u01b0\u1ee3c m\u1ed9t m\u1ec7nh \u0111\u1ec1.<\/p>\n\n\n\n

V\u00ed d\u1ee5 : x = 0 ; y = 1 ta c\u00f3 m\u1ec7nh \u0111\u1ec1 \u00ab 0 + 1 > 1 \u00bb <\/p>\n\n\n\n

x = 1 ; y = 3 ta c\u00f3 m\u1ec7nh \u0111\u1ec1 \u00ab 1 + 3 > 1 \u00bb. <\/p>\n\n\n\n

d) 2 \u2013 \u221a5 < 0 l\u00e0 m\u1ec7nh \u0111\u1ec1 v\u00e0 l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u00fang<\/p>\n\n\n\n

V\u00ec 2 = \u221a4 v\u00e0 \u221a4 < \u221a5. <\/p>\n\n\n\n

Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n

+ M\u1ed7i m\u1ec7nh \u0111\u1ec1 \u0111\u1ec1u c\u00f3 t\u00ednh \u0111\u00fang ho\u1eb7c sai ; kh\u00f4ng th\u1ec3 v\u1eeba \u0111\u00fang v\u1eeba sai. <\/p>\n\n\n\n

+ M\u1ec7nh \u0111\u1ec1 ch\u1ee9a bi\u1ebfn l\u00e0 m\u1ec7nh \u0111\u1ec1 m\u00e0 v\u1edbi m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ebfn s\u1ebd cho ta m\u1ed9t m\u1ec7nh \u0111\u1ec1. <\/p>\n\n\n\n

B\u00e0i 2 (trang 9 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> X\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a m\u1ed7i m\u1ec7nh \u0111\u1ec1 sau v\u00e0 ph\u00e1t bi\u1ec3u m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a n\u00f3:<\/ins><\/p>\n\n\n\n

a) 1794 chia h\u1ebft cho 3 ;\t\t        \tb) \u221a2 l\u00e0 m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9<\/p>\n\n\n\n

c) \u03c0 < 3, 15 ;\t\t        \t\td) |-125| \u2264 0<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/p>\n\n\n\n

a) M\u1ec7nh \u0111\u1ec1 \u00ab 1794 chia h\u1ebft cho 3 \u00bb \u0111\u00fang v\u00ec 1794 : 3 = 598<\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh: “1794 kh\u00f4ng chia h\u1ebft cho 3”<\/p>\n\n\n\n

b) M\u1ec7nh \u0111\u1ec1 \u201c\u221a2 l\u00e0 s\u1ed1 h\u1eefu t\u1ec9\u2019\u2019 sai v\u00ec \u221a2 l\u00e0 s\u1ed1 v\u00f4 t\u1ec9<\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh: “\u221a2 kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9”<\/ins><\/p>\n\n\n\n

c) M\u1ec7nh \u0111\u1ec1 \u03c0 < 3, 15 \u0111\u00fang v\u00ec \u03c0 = 3,141592654\u2026<\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh: “\u03c0 \u2265 3, 15”<\/p>\n\n\n\n

d) M\u1ec7nh \u0111\u1ec1 \u2018\u2019|\u2013125| \u2264 0\u2019\u2019 sai v\u00ec |\u2013125| = 125 > 0<\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh: “|\u2013125| > 0”<\/p>\n\n\n\n

Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n

+ Ta \u0111\u01b0\u1ee3c m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a m\u1ec7nh \u0111\u1ec1 P khi th\u00eam (ho\u1eb7c b\u1edbt) t\u1eeb \u201ckh\u00f4ng\u201d (ho\u1eb7c \u201ckh\u00f4ng ph\u1ea3i\u201d) v\u00e0o tr\u01b0\u1edbc v\u1ecb ng\u1eef c\u1ee7a m\u1ec7nh \u0111\u1ec1 P. <\/p>\n\n\n\n

+ K\u00ed hi\u1ec7u m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a m\u1ec7nh \u0111\u1ec1 P l\u00e0 P\u2212<\/em>. <\/p>\n\n\n\n

+ P \u0111\u00fang th\u00ec P\u2212<\/em> sai v\u00e0 ng\u01b0\u1ee3c l\u1ea1i; P sai th\u00ec P\u2212<\/em> \u0111\u00fang. <\/p>\n\n\n\n

Ki\u1ebfn th\u1ee9c m\u1edf r\u1ed9ng<\/strong><\/p>\n\n\n\n

Ch\u1ee9ng minh \u221a2 l\u00e0 s\u1ed1 v\u00f4 t\u1ec9: <\/p>\n\n\n\n

Gi\u1ea3 s\u1eed \u221a2 l\u00e0 s\u1ed1 h\u1eefu t\u1ec9. <\/p>\n\n\n\n

M\u1ecdi s\u1ed1 h\u1eefu t\u1ec9 \u0111\u1ec1u vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 n\u00ean t\u1ed3n t\u1ea1i s\u1ed1 nguy\u00ean p, q th\u1ecfa m\u00e3n \u221a2 = p\/q v\u1edbi (p; q) = 1. <\/p>\n\n\n\n

Khi \u0111\u00f3 p^{2<\/sup> \/ q2<\/sup> = 2 n\u00ean p2<\/sup> \u22ee 2, suy ra p \u22ee 2. \u0110\u1eb7t p = 2k. <\/p>\n\n\n\n}

Khi \u0111\u00f3 (2k)^{2<\/sup> = 2. q2<\/sup> \u21d2 4k2<\/sup> = 2q2<\/sup> \u21d2 q2<\/sup> = 2k2<\/sup> \u21d2 q2<\/sup> \u22ee 2 \u21d2 q \u22ee 2. <\/p>\n\n\n\n}

V\u1eady p \u22ee2 v\u00e0 q \u22ee 2, tr\u00e1i v\u1edbi \u0111i\u1ec1u ki\u1ec7n (p; q) = 1. <\/p>\n\n\n\n

V\u1eady \u221a2 l\u00e0 s\u1ed1 v\u00f4 t\u1ec9. 8\u2003<\/p>\n\n\n\n

B\u00e0i 3 (trang 9 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> Cho c\u00e1c m\u1ec7nh \u0111\u1ec1 k\u00e9o theo:<\/p>\n\n\n\n

N\u1ebfu a v\u00e0 b c\u00f9ng chia h\u1ebft cho c th\u00ec a + b chia h\u1ebft cho c (a, b, c l\u00e0 nh\u1eefng s\u1ed1 nguy\u00ean).<\/ins><\/p>\n\n\n\n

C\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 c\u00f3 t\u1eadn c\u00f9ng b\u1eb1ng 0 \u0111\u1ec1u chia h\u1ebft cho 5.<\/p>\n\n\n\n

M\u1ed9t tam gi\u00e1c c\u00e2n c\u00f3 hai \u0111\u01b0\u1eddng trung tuy\u1ebfn b\u1eb1ng nhau.<\/p>\n\n\n\n

Hai tam gi\u00e1c b\u1eb1ng nhau c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau.<\/p>\n\n\n\n

a) H\u00e3y ph\u00e1t bi\u1ec3u m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o c\u1ee7a m\u1ed7i m\u1ec7nh \u0111\u1ec1 tr\u00ean.<\/p>\n\n\n\n

b) H\u00e3y ph\u00e1t bi\u1ec3u m\u1ed7i m\u1ec7nh \u0111\u1ec1 tr\u00ean, b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng kh\u00e1i ni\u1ec7m “\u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7”.<\/p>\n\n\n\n

c) Ph\u00e1t bi\u1ec3u m\u1ed7i m\u1ec7nh \u0111\u1ec1 tr\u00ean, b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng kh\u00e1i ni\u1ec7m “\u0111i\u1ec1u ki\u1ec7n c\u1ea7n”.<\/p>\n\n\n\n

L\u1eddi gi\u1ea3i:<\/strong><\/p>\n\n\n\n

M\u1ec7nh \u0111\u1ec1\t<\/td>	M\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o\t<\/td>	Ph\u00e1t bi\u1ec3u b\u1eb1ng kh\u00e1i ni\u1ec7m \u201c \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7\u201d\t<\/td>	Ph\u00e1t bi\u1ec3u b\u1eb1ng kh\u00e1i ni\u1ec7m \u201c\u0111i\u1ec1u ki\u1ec7n c\u1ea7n\u201d<\/td><\/tr>
N\u1ebfu a v\u00e0 b c\u00f9ng chia h\u1ebft cho c th\u00ec a + b chia h\u1ebft cho c.\t<\/td>	N\u1ebfu a + b chia h\u1ebft cho c th\u00ec c\u1ea3 a v\u00e0 b \u0111\u1ec1u chia h\u1ebft cho c.\t<\/td>	a v\u00e0 b chia h\u1ebft cho c l\u00e0 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 \u0111\u1ec3 a + b chia h\u1ebft cho c.\t<\/td>	a + b chia h\u1ebft cho c l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 a v\u00e0 b chia h\u1ebft cho c.<\/td><\/tr>
C\u00e1c s\u1ed1 nguy\u00ean c\u00f3 t\u1eadn c\u00f9ng b\u1eb1ng 0 \u0111\u1ec1u chia h\u1ebft cho 5.\t<\/td>	C\u00e1c s\u1ed1 nguy\u00ean chia h\u1ebft cho 5 th\u00ec c\u00f3 t\u1eadn c\u00f9ng b\u1eb1ng 0.\t<\/td>	M\u1ed9t s\u1ed1 nguy\u00ean t\u1eadn c\u00f9ng b\u1eb1ng 0 l\u00e0 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 \u0111\u1ec3 s\u1ed1 \u0111\u00f3 chia h\u1ebft cho 5.\t<\/td>	C\u00e1c s\u1ed1 nguy\u00ean chia h\u1ebft cho 5 l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 s\u1ed1 \u0111\u00f3 c\u00f3 t\u1eadn c\u00f9ng b\u1eb1ng 0.<\/td><\/tr>
Tam gi\u00e1c c\u00e2n c\u00f3 hai \u0111\u01b0\u1eddng trung tuy\u1ebfn b\u1eb1ng nhau\t<\/td>	Tam gi\u00e1c c\u00f3 hai \u0111\u01b0\u1eddng trung tuy\u1ebfn b\u1eb1ng nhau l\u00e0 tam gi\u00e1c c\u00e2n. \t<\/td>	Tam gi\u00e1c c\u00e2n l\u00e0 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 \u0111\u1ec3 tam gi\u00e1c \u0111\u00f3 c\u00f3 hai \u0111\u01b0\u1eddng trung tuy\u1ebfn b\u1eb1ng nhau.\t<\/td>	“Hai trung tuy\u1ebfn c\u1ee7a m\u1ed9t tam gi\u00e1c b\u1eb1ng nhau l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 tam gi\u00e1c \u0111\u00f3 c\u00e2n.<\/td><\/tr>
Hai tam gi\u00e1c b\u1eb1ng nhau c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau\t<\/td>	Hai tam gi\u00e1c c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau l\u00e0 hai tam gi\u00e1c b\u1eb1ng nhau. \t<\/td>	Hai tam gi\u00e1c b\u1eb1ng nhau l\u00e0 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 \u0111\u1ec3 hai tam gi\u00e1c \u0111\u00f3 c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau.\t<\/td>	Hai tam gi\u00e1c c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 hai tam gi\u00e1c \u0111\u00f3 b\u1eb1ng nhau. <\/td><\/tr><\/tbody><\/table>\n\n\n\n <\/ins><\/p>\n\n\n\n Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n N\u1ebfu ta c\u00f3 m\u1ec7nh \u0111\u1ec1 P \u21d2 Q th\u00ec ta n\u00f3i <\/p>\n\n\n\n + P l\u00e0 \u0111i\u1ec1u ki\u1ec7n \u0111\u1ee7 \u0111\u1ec3 c\u00f3 Q ho\u1eb7c Q l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 c\u00f3 P. <\/p>\n\n\n\n + Q \u21d2 P l\u00e0 m\u1ec7nh \u0111\u1ec1 \u0111\u1ea3o c\u1ee7a m\u1ec7nh \u0111\u1ec1 P \u21d2 Q. <\/p>\n\n\n\n B\u00e0i 4 (trang 9 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> Ph\u00e1t bi\u1ec3u m\u1ed7i m\u1ec7nh \u0111\u1ec1 sau, b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng kh\u00e1i ni\u1ec7m “\u0111i\u1ec1u ki\u1ec7n c\u1ea7n v\u00e0 \u0111\u1ee7”.<\/p>\n\n\n\n a) M\u1ed9t s\u1ed1 c\u00f3 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 chia h\u1ebft cho 9 th\u00ec chia h\u1ebft cho 9 v\u00e0 ng\u01b0\u1ee3c l\u1ea1i.<\/ins><\/p>\n\n\n\n b) M\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 c\u00e1c \u0111\u01b0\u1eddng ch\u00e9o vu\u00f4ng g\u00f3c l\u00e0 m\u1ed9t h\u00ecnh thoi v\u00e0 ng\u01b0\u1ee3c l\u1ea1i.<\/p>\n\n\n\n c) Ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t khi v\u00e0 ch\u1ec9 khi bi\u1ec7t th\u1ee9c c\u1ee7a n\u00f3 d\u01b0\u01a1ng.<\/p>\n\n\n\n L\u1eddi gi\u1ea3i:<\/strong><\/p>\n\n\n\n a)<\/strong> \u0110i\u1ec1u ki\u1ec7n c\u1ea7n v\u00e0 \u0111\u1ee7 \u0111\u1ec3 m\u1ed9t s\u1ed1 chia h\u1ebft cho 9 l\u00e0 t\u1ed5ng c\u00e1c ch\u1eef s\u1ed1 c\u1ee7a n\u00f3 chia h\u1ebft cho 9.<\/p>\n\n\n\n b)<\/strong> M\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 c\u00e1c \u0111\u01b0\u1eddng ch\u00e9o vu\u00f4ng g\u00f3c l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n v\u00e0 \u0111\u1ee7 \u0111\u1ec3 n\u00f3 l\u00e0 m\u1ed9t h\u00ecnh thoi. <\/p>\n\n\n\n c)<\/strong> \u0110\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t, \u0111i\u1ec1u ki\u1ec7n c\u1ea7n v\u00e0 \u0111\u1ee7 l\u00e0 bi\u1ec7t th\u1ee9c c\u1ee7a n\u00f3 d\u01b0\u01a1ng.<\/p>\n\n\n\n Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n + N\u1ebfu P \u21d2 Q v\u00e0 Q \u21d2 P \u0111\u1ec1u \u0111\u00fang th\u00ec ta n\u00f3i P v\u00e0 Q l\u00e0 hai m\u1ec7nh \u0111\u1ec1 t\u01b0\u01a1ng \u0111\u01b0\u01a1ng. <\/p>\n\n\n\n + K\u00ed hi\u1ec7u: P \u21d4 Q \u0111\u1ecdc l\u00e0 P t\u01b0\u01a1ng \u0111\u01b0\u01a1ng v\u1edbi Q, ho\u1eb7c P l\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ea7n v\u00e0 \u0111\u1ee7 \u0111\u1ec3 c\u00f3 Q. <\/p>\n\n\n\n B\u00e0i 5 (trang 10 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> D\u00f9ng k\u00ed hi\u1ec7u \u2200, \u2203 \u0111\u1ec3 vi\u1ebft c\u00e1c m\u1ec7nh \u0111\u1ec1 sau:<\/p>\n\n\n\n a) M\u1ecdi s\u1ed1 nh\u00e2n v\u1edbi 1 \u0111\u1ec1u b\u1eb1ng ch\u00ednh n\u00f3.<\/p>\n\n\n\n b) C\u00f3 m\u1ed9t s\u1ed1 c\u1ed9ng v\u1edbi ch\u00ednh n\u00f3 b\u1eb1ng 0.<\/ins><\/p>\n\n\n\n c) M\u1ecdi s\u1ed1 c\u1ed9ng v\u1edbi s\u1ed1 \u0111\u1ed1i c\u1ee7a n\u00f3 \u0111\u1ec1u b\u1eb1ng 0.<\/p>\n\n\n\n L\u1eddi gi\u1ea3i:<\/strong><\/p>\n\n\n\n a)<\/strong> \u2200 x \u2208 R: x.1 = x<\/p>\n\n\n\n b)<\/strong> \u2203 a \u2208 R: a + a = 0<\/p>\n\n\n\n c)<\/strong> \u2200 x \u2208 R: x + (-x) = 0<\/p>\n\n\n\n Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n + \u2200 : \u0111\u1ecdc l\u00e0 v\u1edbi m\u1ecdi. <\/p>\n\n\n\n + \u2203 : \u0111\u1ecdc l\u00e0 t\u1ed3n t\u1ea1i. \u2003<\/p>\n\n\n\n B\u00e0i 6 (trang 10 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> Ph\u00e1t bi\u1ec3u th\u00e0nh l\u1eddi m\u1ed7i m\u1ec7nh \u0111\u1ec1 sau v\u00e0 x\u00e9t t\u00ednh \u0111\u00fang sai c\u1ee7a n\u00f3.<\/p>\n\n\n\n a) \u2200 x \u2208 R : x2<\/sup> > 0\t;             \t\tb) \u2203 n \u2208 N : n2<\/sup> = n<\/p>\n\n\n\n c) \u2200 n \u2208 N; n \u2264 2n\t             d) \u2203 x \u2208 R : x < 1\/x. <\/p>\n\n\n\n L\u1eddi gi\u1ea3i:<\/strong><\/ins><\/p>\n\n\n\n a) B\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1ecdi s\u1ed1 th\u1ef1c \u0111\u1ec1u d\u01b0\u01a1ng.<\/p>\n\n\n\n \u2013 M\u1ec7nh \u0111\u1ec1 n\u00e0y sai v\u00ec n\u1ebfu x = 0 th\u00ec x2<\/sup> = 0.<\/p>\n\n\n\n S\u1eeda cho \u0111\u00fang: \u2200 x \u2208 R : x2<\/sup> \u2265 0.<\/p>\n\n\n\n b) T\u1ed3n t\u1ea1i s\u1ed1 t\u1ef1 nhi\u00ean m\u00e0 b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a n\u00f3 b\u1eb1ng ch\u00ednh n\u00f3. <\/p>\n\n\n\n \u2013 M\u1ec7nh \u0111\u1ec1 n\u00e0y \u0111\u00fang. V\u00ed d\u1ee5: n = 0; n = 1.<\/ins><\/p>\n\n\n\n c) M\u1ecdi s\u1ed1 t\u1ef1 nhi\u00ean \u0111\u1ec1u nh\u1ecf h\u01a1n ho\u1eb7c b\u1eb1ng hai l\u1ea7n c\u1ee7a n\u00f3. <\/p>\n\n\n\n \u2013 M\u1ec7nh \u0111\u1ec1 n\u00e0y \u0111\u00fang.<\/p>\n\n\n\n d) T\u1ed3n t\u1ea1i s\u1ed1 th\u1ef1c nh\u1ecf h\u01a1n ngh\u1ecbch \u0111\u1ea3o c\u1ee7a ch\u00ednh n\u00f3. <\/p>\n\n\n\n \u2013 M\u1ec7nh \u0111\u1ec1 n\u00e0y \u0111\u00fang. V\u00ed d\u1ee5 0,5 < 1\/ 0,5. <\/p>\n\n\n\n Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n + \u2200 : \u0111\u1ecdc l\u00e0 v\u1edbi m\u1ecdi. <\/p>\n\n\n\n + \u2203 : \u0111\u1ecdc l\u00e0 t\u1ed3n t\u1ea1i. \u2003<\/p>\n\n\n\n B\u00e0i 7 (trang 10 SGK \u0110\u1ea1i s\u1ed1 10):<\/strong> L\u1eadp m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a c\u00e1c m\u1ec7nh \u0111\u1ec1 sau v\u00e0 x\u00e9t t\u00ednh \u0111\u00fang, sai c\u1ee7a n\u00f3:<\/p>\n\n\n\n a) \u2200 n \u2208 N: n chia h\u1ebft cho n\t;        \tb) \u2203 x \u2208 Q : x2<\/sup> = 2<\/ins><\/p>\n\n\n\n c) \u2200 x \u2208 R : x < x + 1\t;        \td) \u2203 x \u2208 R: 3x = x2<\/sup> + 1<\/p>\n\n\n\n L\u1eddi gi\u1ea3i:<\/strong><\/p>\n\n\n\n a) A: \u201c\u2200 n \u2208 N: n chia h\u1ebft cho n\u201d<\/p>\n\n\n\n A\u2212 : \u201c\u2203 n \u2208 N: n kh\u00f4ng chia h\u1ebft cho n\u201d.<\/p>\n\n\n\n A\u2212 \u0111\u00fang v\u00ec v\u1edbi n = 0 th\u00ec n kh\u00f4ng chia h\u1ebft cho n. <\/p>\n\n\n\n b) B: \u201c\u2203 x \u2208 Q : x2<\/sup> = 2\u201d. <\/p>\n\n\n\n B\u2212 : \u201c\u2200 x \u2208 Q : x2<\/sup> \u2260 2\u201d<\/p>\n\n\n\n B\u2212 \u0111\u00fang. <\/p>\n\n\n\n L\u01b0u \u00fd: \u221a2 l\u00e0 s\u1ed1 v\u00f4 t\u1ef7. <\/ins><\/p>\n\n\n\n c) C: \u201c\u2200 x \u2208 R : x < x + 1\u201d. <\/p>\n\n\n\n C\u2212 : \u201c\u2203 x \u2208 R: x \u2265 x + 1\u201d.<\/p>\n\n\n\n C\u2212 sai v\u00ec x + 1 lu\u00f4n l\u1edbn h\u01a1n x. <\/p>\n\n\n\n d) D: \u201c\u2203 x \u2208 R: 3x = x2<\/sup> + 1\u201d <\/p>\n\n\n\n D\u2212 : \u201c\u2200 x \u2208 R ; 3x \u2260 x2<\/sup> + 1\u201d<\/p>\n\n\n\n <\/figure>\n\n\n\n D\u2212 sai v\u00ec v\u1edbi <\/p>\n\n\n\n D\u2212 th\u1ecfa m\u00e3n: <\/p>\n\n\n\n <\/figure>\n\n\n\n Ki\u1ebfn th\u1ee9c \u00e1p d\u1ee5ng<\/strong><\/p>\n\n\n\n + K\u00ed hi\u1ec7u P\u2212 l\u00e0 m\u1ec7nh \u0111\u1ec1 ph\u1ee7 \u0111\u1ecbnh c\u1ee7a m\u1ec7nh \u0111\u1ec1 P. <\/p>\n\n\n\n <\/figure>\n\n\n\n + N\u1ebfu A: \u201c\u2200 x \u2208 X, P(x)\u201d th\u00ec A\u2212: \u201c\u2203 x \u2208 X, \u201d<\/p>\n\n\n\n <\/figure>\n\n\n\n + N\u1ebfu A: \u201c\u2203 x \u2208 X, Q(x)\u201d th\u00ec A\u2212: \u201c\u2200 x \u2208 X, \u201d. <\/p>\n","protected":false},"excerpt":{"rendered":" Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 1 trang 4: Nh\u00ecn v\u00e0o hai b\u1ee9c tranh \u1edf tr\u00ean, h\u00e3y \u0111\u1ecdc v\u00e0 so s\u00e1nh c\u00e1c c\u00e2u \u1edf b\u00ean tr\u00e1i v\u00e0 b\u00ean ph\u1ea3i. L\u1eddi gi\u1ea3i C\u00e1c c\u00e2u \u1edf b\u00ean tr\u00e1i l\u00e0 c\u00e1c c\u00e2u kh\u1eb3ng \u0111\u1ecbnh, c\u00f3 t\u00ednh \u0111\u00fang sai C\u00e1c c\u00e2u \u1edf b\u00ean ph\u1ea3i kh\u00f4ng th\u1ec3 […]<\/p>\n","protected":false},"author":12,"featured_media":44298,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1633],"tags":[],"yoast_head":"\n