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{"id":44344,"date":"2019-10-16T15:55:00","date_gmt":"2019-10-16T08:55:00","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=44344"},"modified":"2019-10-16T15:55:06","modified_gmt":"2019-10-16T08:55:06","slug":"giai-toan-10-chuong-4-bat-dang-thuc-bat-phuong-trinh-bai-4-bat-phuong-trinh-bac-nhat-hai-an","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/giai-toan-10-chuong-4-bat-dang-thuc-bat-phuong-trinh-bai-4-bat-phuong-trinh-bac-nhat-hai-an\/","title":{"rendered":"[Gi\u1ea3i To\u00e1n 10] Ch\u01b0\u01a1ng 4: B\u1ea5t \u0111\u1eb3ng th\u1ee9c. B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh\/ B\u00e0i 4: B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n"},"content":{"rendered":"\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 4 trang 96<\/strong>: Bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc t\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n: -3x + 2y > 0.<\/ins><\/p>\n\n\n\n

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

V\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng (d): -3x + 2y = 0<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

L\u1ea5y \u0111i\u1ec3m A(1; 1), ta th\u1ea5y A \u2209(d) v\u00e0 c\u00f3: -3.1 + 2.1 < 0 n\u00ean n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd (d) kh\u00f4ng ch\u01b0\u00e1 A l\u00e0 mi\u1ec1n nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh. (mi\u1ec1n h\u00ecnh kh\u00f4ng b\u1ecb t\u00f4 \u0111\u1eadm)<\/p>\n\n\n\n

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 4 trang 97<\/strong>: Bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc t\u1eadp nghi\u1ec7m c\u1ee7a h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/ins><\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

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

\"Gi\u1ea3i<\/figure>\n\n\n\n
\"Gi\u1ea3i<\/figure>\n\n\n\n

L\u1ea5y \u0111i\u1ec3m O(0;0), ta th\u1ea5y O kh\u00f4ng thu\u1ed9c c\u1ea3 2 \u0111\u01b0\u1eddng th\u1eb3ng tr\u00ean v\u00e0 2.0-0 \u2264 3 v\u00e0 -2.0 + 0 \u2264 8\/5 n\u00ean ph\u1ea7n \u0111\u01b0\u1ee3c gi\u1edbi h\u1ea1n b\u1edfi 2 \u0111\u01b0\u1eddng th\u1eb3ng tr\u00ean ch\u1ee9a \u0111i\u1ec3m O( ph\u1ea7n ko t\u00f4 \u0111\u1eadm) l\u00e0 nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n\n\n\n

B\u00e0i 1 (trang 99 SGK \u0110\u1ea1i S\u1ed1 10)<\/strong>: Bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc t\u1eadp nghi\u1ec7m c\u1ee7a c\u00e1c b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n sau:<\/p>\n\n\n\n

a) -x + 2 + 2(y – 2) < 2(1 – x)<\/ins><\/p>\n\n\n\n

b) 3(x – 1) + 4(y – 2) < 5x – 3<\/p>\n\n\n\n

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

a) \u2013x + 2 + 2(y \u2013 2) < 2(1 \u2013 x)<\/p>\n\n\n\n

\u21d4 \u2013x + 2 + 2y \u2013 4 < 2 \u2013 2x<\/p>\n\n\n\n

\u21d4 x + 2y < 4 (1) <\/p>\n\n\n\n

Bi\u1ec3u di\u1ec5n t\u1eadp nghi\u1ec7m tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 : <\/p>\n\n\n\n

\u2013 V\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng x + 2y = 4. <\/p>\n\n\n\n

\u2013 Thay t\u1ecda \u0111\u1ed9 (0; 0) v\u00e0o (1) ta \u0111\u01b0\u1ee3c 0 + 0 < 4 <\/p>\n\n\n\n

\u21d2 (0; 0) l\u00e0 m\u1ed9t nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n\n\n\n

V\u1eady mi\u1ec1n nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 n\u1eeda m\u1eb7t ph\u1eb3ng ch\u1ee9a g\u1ed1c t\u1ecda \u0111\u1ed9\n kh\u00f4ng k\u1ec3 b\u1edd v\u1edbi b\u1edd l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x + 2y = 4 (mi\u1ec1n kh\u00f4ng b\u1ecb g\u1ea1ch). <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

<\/ins><\/p>\n\n\n\n

b) 3(x \u2013 1) + 4(y \u2013 2) < 5x \u2013 3<\/p>\n\n\n\n

\u21d4 3x \u2013 3 + 4y \u2013 8 < 5x \u2013 3<\/p>\n\n\n\n

\u21d4 2x \u2013 4y > \u20138<\/p>\n\n\n\n

\u21d4 x \u2013 2y > \u20134<\/p>\n\n\n\n

Bi\u1ec3u di\u1ec5n t\u1eadp nghi\u1ec7m tr\u00ean m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9:<\/p>\n\n\n\n

\u2013 V\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng x \u2013 2y = \u20134. <\/p>\n\n\n\n

\u2013 Thay t\u1ecda \u0111\u1ed9 (0; 0) v\u00e0o (2) ta \u0111\u01b0\u1ee3c: 0 + 0 > \u20134 \u0111\u00fang<\/p>\n\n\n\n

\u21d2 (0; 0) l\u00e0 m\u1ed9t nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n\n\n\n

V\u1eady mi\u1ec1n nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 n\u1eeda m\u1eb7t ph\u1eb3ng ch\u1ee9a g\u1ed1c t\u1ecda \u0111\u1ed9 kh\u00f4ng k\u1ec3 b\u1edf v\u1edbi b\u1edd l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng x \u2013 2y = \u20134<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

B\u00e0i 2 (trang 99 SGK \u0110\u1ea1i S\u1ed1 10)<\/strong>: Bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc t\u1eadp nghi\u1ec7m c\u1ee7a c\u00e1c h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n sau:<\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

a) <\/ins><\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

b) <\/p>\n\n\n\n

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

\"Gi\u1ea3i<\/figure>\n\n\n\n

Ta v\u1ebd c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng x \u2013 2y = 0 (d1<\/sub>) ; x + 3y = \u20132 (d2<\/sub>) ; \u2013x + y = 3 (d3<\/sub>). <\/p>\n\n\n\n

\u0110i\u1ec3m A(\u20131; 0) c\u00f3 t\u1ecda \u0111\u1ed9 th\u1ecfa m\u00e3n t\u1ea5t c\u1ea3 c\u00e1c b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh trong h\u1ec7 n\u00ean ta g\u1ea1ch \u0111i c\u00e1c n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd (d1<\/sub>); (d2<\/sub>); (d3<\/sub>) kh\u00f4ng ch\u1ee9a \u0111i\u1ec3m A. <\/p>\n\n\n\n

Mi\u1ec1n kh\u00f4ng b\u1ecb g\u1ea1ch ch\u00e9o trong h\u00ecnh v\u1ebd, kh\u00f4ng t\u00ednh c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 mi\u1ec1n nghi\u1ec7m c\u1ee7a h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho. <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

<\/ins><\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

Ta v\u1ebd c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng 2x + 3y = 6 (d1<\/sub>); 2x \u2013 3y = 3 (d2<\/sub>); x = 0 (tr\u1ee5c tung). <\/p>\n\n\n\n

\u0110i\u1ec3m B(1; 0) c\u00f3 t\u1ecda \u0111\u1ed9 th\u1ecfa m\u00e3n t\u1ea5t c\u1ea3 c\u00e1c b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh trong h\u1ec7 n\u00ean ta g\u1ea1ch \u0111i c\u00e1c n\u1eeda m\u1eb7t ph\u1eb3ng b\u1edd (d1<\/sub>); (d2<\/sub>) v\u00e0 tr\u1ee5c tung kh\u00f4ng ch\u1ee9a \u0111i\u1ec3m B.<\/ins><\/p>\n\n\n\n

Mi\u1ec1n kh\u00f4ng b\u1ecb g\u1ea1ch ch\u00e9o (tam gi\u00e1c MNP, k\u1ec3 c\u1ea3 c\u1ea1nh MP v\u00e0 NP, kh\u00f4ng k\u1ec3 c\u1ea1nh MN) l\u00e0 mi\u1ec1n nghi\u1ec7m c\u1ee7a h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh \u0111\u00e3 cho. <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

B\u00e0i 3 (trang 99 SGK \u0110\u1ea1i S\u1ed1 10)<\/strong>: C\u00f3 ba \nnh\u00f3m m\u00e1y A, B, C d\u00f9ng \u0111\u1ec3 s\u1ea3n xu\u1ea5t ra hai lo\u1ea1i s\u1ea3n ph\u1ea9m I v\u00e0 II. \u0110\u1ec3 s\u1ea3n \nxu\u1ea5t m\u1ed9t \u0111\u01a1n v\u1ecb s\u1ea3n ph\u1ea9m m\u1ed7i lo\u1ea1i l\u1ea7n l\u01b0\u1ee3t ph\u1ea3i d\u00f9ng c\u00e1c m\u00e1y thu\u1ed9c c\u00e1c \nnh\u00f3m kh\u00e1c nhau. S\u1ed1 m\u00e1y trong m\u1ed9t nh\u00f3m v\u00e0 s\u1ed1 m\u00e1y c\u1ee7a t\u1eebng nh\u00f3m c\u1ea7n thi\u1ebft \n\u0111\u1ec3 s\u1ea3n xu\u1ea5t ra m\u1ed9t \u0111\u01a1n v\u1ecb s\u1ea3n ph\u1ea9m thu\u1ed9c m\u1ed7i lo\u1ea1i \u0111\u01b0\u1ee3c d\u00f9ng cho trong \nb\u1ea3ng sau:<\/ins><\/p>\n\n\n\n
Nh\u00f3m<\/td>S\u1ed1 m\u00e1y trong m\u1ed7i nh\u00f3m<\/td>S\u1ed1 m\u00e1y trong t\u1eebng nh\u00f3m \u0111\u1ec3 s\u1ea3n xu\u1ea5t ra m\u1ed9t \u0111\u01a1n v\u1ecb s\u1ea3n ph\u1ea9m<\/td><\/tr>
Lo\u1ea1i I<\/td>Lo\u1ea1i II<\/td><\/tr>
A<\/td>10<\/td>2<\/td>2<\/td><\/tr>
B<\/td>4<\/td>0<\/td>2<\/td><\/tr>
C<\/td>12<\/td>2<\/td>4<\/td><\/tr><\/tbody><\/table>\n\n\n\n

M\u1ed9t \u0111\u01a1n v\u1ecb s\u1ea3n ph\u1ea9m I l\u00e3i 3 ngh\u00ecn \u0111\u1ed3ng, m\u1ed9t \u0111\u01a1n v\u1ecb s\u1ea3n xu\u1ea5t II l\u00e3i 5 \nngh\u00ecn \u0111\u1ed3ng. H\u00e3y l\u1eadp k\u1ebf ho\u1ea1ch s\u1ea3n xu\u1ea5t \u0111\u1ec3 cho t\u1ed5ng s\u1ed1 ti\u1ec1n l\u00e3i cao nh\u1ea5t.<\/p>\n\n\n\n

H\u01b0\u1edbng d\u1eabn:<\/em> \u00c1p d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i trong m\u1ee5c IV.<\/p>\n\n\n\n

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

G\u1ecdi x l\u00e0 s\u1ed1 \u0111\u01a1n v\u1ecb s\u1ea3n ph\u1ea9m lo\u1ea1i I, y l\u00e0 s\u1ed1 \u0111\u01a1n v\u1ecb s\u1ea3n ph\u1ea9m lo\u1ea1i II s\u1ea3n xu\u1ea5t ra. <\/p>\n\n\n\n

Nh\u01b0 v\u1eady ti\u1ec1n l\u00e3i c\u00f3 \u0111\u01b0\u1ee3c l\u00e0 L = 3x + 5y (ngh\u00ecn \u0111\u1ed3ng).<\/p>\n\n\n\n

Theo \u0111\u1ec1 b\u00e0i: Nh\u00f3m A c\u1ea7n 2x + 2y m\u00e1y; <\/p>\n\n\n\n

Nh\u00f3m B c\u1ea7n 0x + 2y m\u00e1y; <\/p>\n\n\n\n

Nh\u00f3m C c\u1ea7n 2x + 4y m\u00e1y; <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

V\u00ec s\u1ed1 m\u00e1y t\u1ed1i \u0111a \u1edf nh\u00f3m A l\u00e0 10 m\u00e1y, nh\u00f3m B l\u00e0 4 m\u00e1y, nh\u00f3m C l\u00e0 12 m\u00e1y n\u00ean x, y ph\u1ea3i th\u1ecfa m\u00e3n h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: \n<\/ins><\/p>\n\n\n\n

Khi \u0111\u00f3 b\u00e0i to\u00e1n tr\u1edf th\u00e0nh: trong c\u00e1c nghi\u1ec7m c\u1ee7a h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh (1) th\u00ec nghi\u1ec7m (x = xo<\/sub>; y = yo<\/sub>) n\u00e0o cho L = 3x + 5y l\u1edbn nh\u1ea5t.<\/p>\n\n\n\n

Mi\u1ec1n nghi\u1ec7m c\u1ee7a h\u1ec7 b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh (1) l\u00e0 ng\u0169 gi\u00e1c ABCDE k\u1ec3 c\u1ea3 mi\u1ec1n trong. <\/p>\n\n\n\n

\"Gi\u1ea3i<\/figure>\n\n\n\n

Ta c\u00f3: L \u0111\u1ea1t gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t t\u1ea1i m\u1ed9t trong c\u00e1c \u0111\u1ec9nh c\u1ee7a t\u1ee9 gi\u00e1c ABCDE. <\/p>\n\n\n\n

T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c L = 3x + 5y t\u1ea1i c\u00e1c \u0111\u1ec9nh ta \u0111\u01b0\u1ee3c: <\/p>\n\n\n\n

T\u1ea1i \u0111\u1ec9nh A(0;2), L = 10<\/p>\n\n\n\n

T\u1ea1i \u0111\u1ec9nh B(2; 2), L = 16 <\/p>\n\n\n\n

T\u1ea1i \u0111\u1ec9nh C(4; 1), L = 17<\/p>\n\n\n\n

T\u1ea1i \u0111\u1ec9nh D(5; 0), L = 15<\/p>\n\n\n\n

T\u1ea1i \u0111\u1ec9nh E(0; 0), L = 0. <\/p>\n\n\n\n

Do \u0111\u00f3, L = 3x + 5y l\u1edbn nh\u1ea5t l\u00e0 17 (ngh\u00ecn \u0111\u1ed3ng) khi: x = 4; y = 1<\/p>\n\n\n\n

V\u1eady \u0111\u1ec3 c\u00f3 ti\u1ec1n l\u00e3i cao nh\u1ea5t, c\u1ea7n s\u1ea3n xu\u1ea5t 4 \u0111\u01a1n v\u1ecb s\u1ea3n ph\u1ea9m lo\u1ea1i I v\u00e0 1 \u0111\u01a1n v\u1ecb s\u1ea3n ph\u1ea9m lo\u1ea1i II<\/p>\n","protected":false},"excerpt":{"rendered":"

Tr\u1ea3 l\u1eddi c\u00e2u h\u1ecfi To\u00e1n 10 \u0110\u1ea1i s\u1ed1 B\u00e0i 4 trang 96: Bi\u1ec3u di\u1ec5n h\u00ecnh h\u1ecdc t\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n: -3x + 2y > 0. L\u1eddi gi\u1ea3i V\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng (d): -3x + 2y = 0 L\u1ea5y \u0111i\u1ec3m A(1; 1), ta th\u1ea5y A \u2209(d) v\u00e0 c\u00f3: -3.1 + 2.1 […]<\/p>\n","protected":false},"author":12,"featured_media":44345,"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[Gi\u1ea3i To\u00e1n 10] Ch\u01b0\u01a1ng 4: B\u1ea5t \u0111\u1eb3ng th\u1ee9c. B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh\/ B\u00e0i 4: B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t hai \u1ea9n<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/giai-toan-10-chuong-4-bat-dang-thuc-bat-phuong-trinh-bai-4-bat-phuong-trinh-bac-nhat-hai-an\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"[Gi\u1ea3i To\u00e1n 10] Ch\u01b0\u01a1ng 4: B\u1ea5t \u0111\u1eb3ng th\u1ee9c. 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