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{"id":23702,"date":"2018-03-26T18:22:34","date_gmt":"2018-03-26T11:22:34","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=23702"},"modified":"2018-03-26T18:22:34","modified_gmt":"2018-03-26T11:22:34","slug":"dai-so-chuong-1-bai-8-mot-so-bai-toan-thuong-gap-ve-do-thi","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/dai-so-chuong-1-bai-8-mot-so-bai-toan-thuong-gap-ve-do-thi\/","title":{"rendered":"\u0110\u1ea1i s\u1ed1 – Ch\u01b0\u01a1ng 1 – B\u00e0i 8: M\u1ed9t s\u1ed1 b\u00e0i to\u00e1n th\u01b0\u1eddng g\u1eb7p v\u1ec1 \u0111\u1ed3 th\u1ecb"},"content":{"rendered":"

B\u00e0i 57 (trang 55 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 \u0111\u1ed3 th\u1ecb (C) h\u00e0m s\u1ed1: f(x)=2x3<\/sup>+3x2<\/sup>+1<\/p>\n

b) T\u00ecm c\u00e1c giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng cong (C) v\u00e0 parapol g(x) = 2x2<\/sup>+1 (P)<\/p>\n

c) Vi\u1ebft Ph\u01b0\u01a1ng tr\u00ecnh c\u00e1c ti\u1ebfp \u0111i\u1ec3m c\u1ee7a (C) v\u00e0 (P) t\u1ea1i c\u00e1c \u0111i\u1ec3m c\u1ee7a ch\u00fang.<\/p>\n

d) X\u00e1c \u0111\u1ecbnh c\u00e1c kho\u1ea3ng tr\u00ean \u0111\u00f3 (C) n\u1eb1m ph\u00eda tr\u00ean v\u00e0 ho\u1eb7c ph\u00eda d\u01b0\u1edbi (P).<\/p>\n

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

a) H\u00e0m s\u1ed1: f(x) = y=2x3<\/sup>+3x2<\/sup>+1. TX\u0110: D = R<\/p>\n

S\u1ef1 bi\u1ebfn thi\u00ean: y\u2019 = 6x2<\/sup>+6x<\/p>\n

\"\"<\/p>\n

S\u1ef1 bi\u1ebfn thi\u00ean, ngh\u1ecbch bi\u1ebfn.<\/p>\n

H\u00e0m s\u1ed1 \u0111\u1ed3ng bi\u1ebfn trong kho\u1ea3ng (-\u221e; -1)v\u00e0 (0;+\u221e)<\/p>\n

H\u00e0m s\u1ed1 ngh\u1ecbch bi\u1ebfn trong kho\u1ea3ng (-1; 0)<\/p>\n

C\u1ef1c tr\u1ecb: yC\u0110<\/sub>=2 khi x = -1<\/p>\n

yCT<\/sub>=1 khi x = 1v<\/p>\n

\"\"<\/p>\n

\u0110i\u1ec3m u\u1ed1n, t\u00ednh l\u1ed3i l\u00f5m:<\/p>\n

Ta c\u00f3 y\u2019\u2019 = 12x + 6<\/p>\n

y”=0 <=> 12x+6=0 <=> x=-1\/2 => y=3\/2<\/p>\n

B\u1ea3ng x\u00e9t d\u1ea5u<\/p>\n

\"\"<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean<\/p>\n

\"\"<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1 : f(x) = y = 2x3<\/sup>+3x2<\/sup>+1<\/p>\n

Giao \u0111i\u1ec3m Oy: (0; 1)<\/p>\n

\u0110i qua (-1; 2)<\/p>\n

\"\"<\/p>\n

b) Ho\u00e0nh \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng cong (C) v\u00e0 parabol (P) l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n

f(x)=g(x) <=> 2x3<\/sup>+3x2<\/sup>+1=2x2<\/sup>+1<\/p>\n

\"\"<\/p>\n

V\u1eady \u0111\u01b0\u1eddng cong C v\u00e0 parabol (P) c\u1eaft t\u1ea1i 2 \u0111i\u1ec3m: A(0; 1); B(-1\/2;3\/2)<\/p>\n

c) H\u1ec7 s\u1ed1 g\u00f3c ti\u1ebfp tuy\u1ebfn t\u1ea1i \u0111i\u1ec3m A c\u1ee7a \u0111\u01b0\u1eddng cong (C ) v\u00e0 parabol (P) l\u00e0: y\u2019(0) = 0<\/p>\n

V\u1eady Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn t\u1ea1i giao \u0111i\u1ec3m A c\u1ee7a \u0111\u01b0\u1eddng cong (C) v\u00e0 parabol (P) y0(x-0)+1,hay y=1<\/p>\n

H\u1ec7 s\u1ed1 s\u1ed1 g\u00f3c ti\u1ebfp tuy\u1ebfn t\u1ea1i giao \u0111i\u1ec3m A c\u1ee7a \u0111\u01b0\u1eddng cong (C) v\u00e0 parabol (P) l\u00e0:<\/p>\n

\"\"<\/p>\n

V\u1eady Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn t\u1ea1i giao \u0111i\u1ec3m B c\u1ee7a \u0111\u01b0\u1eddng cong (C) v\u00e0 parabol (P) l\u00e0:<\/p>\n

\"\"<\/p>\n

d) \u0110\u1ec3 (C) n\u1eb1m ph\u00eda tr\u00ean (P) th\u00ec 2 h\u00e0m s\u1ed1 f(x) v\u00e0 g(x) ph\u1ea3i th\u00f5a m\u00e3n \u0111i\u1ec1u ki\u1ec7n sau:<\/p>\n

\"\"<\/p>\n

V\u1eady v\u1edbi x \u2208(-\u221e; -1\/2) v\u00e0 (0; +\u221e) th\u00ec (C) n\u1eb1m ph\u00eda tr\u00ean (P). \u0110\u1ec3 (C) n\u1eb1m ph\u00eda d\u01b0\u1edbi (P) th\u00ec 2 h\u00e0m s\u1ed1 f(x) v\u00e0 g(x) th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n sau:<\/p>\n

f(x)< g(x) <=> 2x3<\/sup>+3x2<\/sup>+1 < 2x2<\/sup>+1 <=> 2x3<\/sup>+x2<\/sup>\u00a0< 0 <=> -1\/2 < x < 0<\/p>\n

V\u1eady v\u1edbi x \u2208(-1\/2;0) th\u00ec (C) n\u1eb1m ph\u00eda d\u01b0\u1edbi (P).<\/p>\n

\n
\n

B\u00e0i 58 (trang 56 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 v\u1ebd \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1<\/p>\n

\"\"<\/p>\n

b) V\u1edbi c\u00e1c gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a m th\u00ec (dm<\/sub>) \u0111i qua \u0111i\u1ec3m A(-2; 2) v\u00e0 c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c m c\u1eaft \u0111\u1ed3 th\u1ecb c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00e3 cho.<\/p>\n

– T\u1ea1i 2 \u0111i\u1ec3m ph\u1eadn bi\u1ec7t?<\/p>\n

– T\u1ea1i 2 \u0111i\u1ec3m thu\u1ed9c 2 nh\u00e1nh 2 c\u1ee7a \u0111\u1ed3 th\u1ecb?<\/p>\n

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

\"\"<\/p>\n

– H\u00e0m s\u1ed1 lu\u00f4n \u0111\u1ed3ng \u0111\u1ed3ng bi\u1ebfn trong kho\u1ea3ng (-\u221e; -1)v\u00e0 (-1;+\u221e)<\/p>\n

– H\u00e0m s\u1ed1 kh\u00f4ng c\u00f3 c\u1ef1c tr\u1ecb.<\/p>\n

\"\"<\/p>\n

V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn \u0111\u1ee9ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng: x = -1.<\/p>\n

\"\"<\/p>\n

V\u1eady \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 c\u00f3 ti\u1ec7m c\u1eadn ngang l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng: y = 2.<\/p>\n

B\u1ea3ng bi\u1ebfn thi\u00ean<\/p>\n

\"\"<\/p>\n

\u0110\u1ed3 th\u1ecb h\u00e0m s\u1ed1<\/p>\n

\"\"<\/p>\n

nh\u1eadn \u0111i\u1ec3m I l\u00e0 giao \u0111i\u1ec3m c\u1ee7a 2 ti\u1ec7m c\u1eadn l\u00e0m t\u00e2m \u0111\u1ed1i x\u1ee9ng I(-1; 2). \u0110\u1ed3 th\u1ecb \u0111i qua A(0; -1), B(1\/2;0),C(1;1\/2);D(2;1)<\/p>\n

\"\"<\/p>\n

b) \u0110\u01b0\u1eddng th\u1eb3ng (dm<\/sub>) qua \u0111i\u1ec3m A(-2; 2) c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c m l\u00e0:<\/p>\n

y=m(x+2)+2<\/p>\n

<=> y=mx+2m+2<\/p>\n

\u0110\u1ec3 (dm<\/sub>) c\u1eaft \u0111\u1ed3 th\u1ecb (C) t\u1ea1i 2 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t th\u00ec ph\u01b0\u01a1ng tr\u00ecnh sau ph\u1ea3i c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t \u2260 -1<\/p>\n

\"\"<\/p>\n

<=> f(x)=mx2<\/sup>+3mx+2m+3=0 (1)<\/p>\n

V\u00e0 f(-1) \u2260 0<\/p>\n

\u0110\u1ec3 (1) c\u00f3 2 nghi\u1ec7m ph\u00e2n bi\u1ec7t th\u00ec: \u0394>0,f(-1) \u2260 0<\/p>\n

Ta c\u00f3: \u0394=(3m)2<\/sup>-4(2m+3)m>0<\/p>\n

= m2<\/sup>-12m>0<\/p>\n

\"\"<\/p>\n

V\u1eady v\u1edbi m \u2208(-\u221e;0) v\u00e0 (12,+\u221e) th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng (dm<\/sub>) s\u1ebd c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 (C) t\u1ea1i 2 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t.<\/p>\n

– \u0110\u1ec3 (dm<\/sub>) c\u1eaft \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 (C) t\u1ea1i 2 \u0111i\u1ec3m thu\u1ed9c 2 nh\u00e1nh c\u1ee7a \u0111\u1ed3 th\u1ecb th\u00ec:<\/p>\n

x1<\/sub><-1<x2<\/sub>\u00a0hay af(-1)<0<\/p>\n

<=> m(m(-1)2<\/sup>+3m(-1)+2m+3)<0 <=> 3m<0 <=> m < 0<\/p>\n

V\u1eady v\u1edbi m \u2208(-\u221e;0) th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng (dm<\/sub>) s\u1ebd c\u1eaft \u0111\u1ed3 th\u1ecb (C) t\u1ea1i 2 \u0111i\u1ec3m ph\u00e2n bi\u1ec7t \u2208 2 nh\u00e1nh \u0111\u1ed3 th\u1ecb.<\/p>\n

B\u00e0i 59 (trang 56 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\n

Ch\u1ee9ng minh r\u1eb1ng c\u00e1c \u0111\u1ed3 th\u1ecb c\u1ee7a 3 h\u00e0m s\u1ed1: f(x) = -x2<\/sup>+3x+6;g(x)=x3<\/sup>-x2<\/sup>+4 v\u00e0 h(x) = x2<\/sup>+7x+8 ti\u1ebfp x\u00fac v\u1edbi nhau t\u1ea1i \u0111i\u1ec3m A(-1; 2)<\/p>\n

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

N\u1ebfu 3 h\u00e0m s\u1ed1 tr\u00ean ti\u1ebfp x\u00fac v\u1edbi nhau t\u1ea1i A(-1; 2) th\u00ec t\u1ea1i \u0111\u00f3 3 h\u00e0m s\u1ed1 c\u00f3 ti\u1ebfp tuy\u1ebfn chung hay h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a c\u00e1c ti\u1ebfp tuy\u1ebfn b\u1eb1ng nhau. Ta c\u00f3:<\/p>\n

+ f\u2019(x) = -2x+3=>f’ (-1)=5<\/p>\n

+ g\u2019(x) = 3x2<\/sup>-2x=>g’ (-1)=5<\/p>\n

+ h\u2019(x) = 2x+7=>h’ (-1)=5<\/p>\n

V\u1eady 3 h\u00e0m s\u1ed1 tr\u00ean ti\u1ebfp x\u00fac v\u1edbi nhau nhau t\u1ea1i A(-1; 2)<\/p>\n

\n
\n

B\u00e0i 60 (trang 56 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b><\/span><\/p>\n

Ch\u1ee9ng minh r\u1eb1ng c\u00e1c \u0111\u1ed3 th\u1ecb c\u1ee7a hai h\u00e0m s\u1ed1<\/p>\n

\"\"<\/p>\n

ti\u1ebfp x\u00fac v\u1edbi nhau. X\u00e1c \u0111\u1ecbnh ti\u1ebfp tuy\u1ebfn c\u1ee7a 2 \u0111\u01b0\u1eddng cong tr\u00ean v\u00e0 vi\u1ebft Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn chung c\u1ee7a ch\u00fang t\u1ea1i \u0111i\u1ec3m \u0111\u00f3.<\/p>\n

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

Hai h\u00e0m s\u1ed1 f(x) v\u00e0 g(x) ti\u1ebfp x\u00fac v\u1edbi nhau khi v\u00e0 ch\u1ec9 khi h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh sau c\u00f3 nghi\u1ec7m:<\/p>\n

\"\"<\/p>\n

V\u1eady ti\u1ebfp tuy\u1ebfn c\u1ee7a 2 \u0111\u01b0\u1eddng cong tr\u00ean l\u00e0 M(0; 0)<\/p>\n

Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn chung c\u1ee7a f(x) v\u00e0 g(x) c\u00f3 h\u1ec7 s\u1ed1 g\u00f3c k l\u00e0: k = f\u2019(0) = 3\/2<\/p>\n

V\u1eady Ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn chung c\u1ee7a f(x) v\u00e0 g(x) l\u00e0: y=3x\/2<\/p>\n

B\u00e0i 61 (trang 56 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao):<\/b>\u00a0<\/span><\/p>\n

M\u1ed9t vi\u00ean \u0111\u1ea1n \u0111\u01b0\u1ee3c b\u1eafn ra v\u1edbi v\u1eadn t\u1ed1c ban \u0111\u1ea7u v_0>0 t\u1eeb m\u1ed9t n\u00f2ng sung \u0111\u1eb7t \u1edf g\u1ed1c t\u1ecda \u0111\u1ed9 O, nghi\u00eang m\u1ed9t g\u00f3c \u03b1 v\u1edbi m\u1eb7t \u0111\u1ea5t (n\u00f2ng s\u00fang n\u1eb1m trong m\u1eb7t ph\u1eb3ng \u0111\u1ee9ng th\u1eb3ng Oxy v\u00e0 t\u1ea1o v\u1edbi tr\u1ee5c ho\u00e0nh Ox m\u1ed9t g\u00f3c \u03b1. Bi\u1ebft qu\u1ef9 \u0111\u1ea1o chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a vi\u00ean \u0111\u1ea1n l\u00e0 parabol.<\/p>\n

\"\"<\/p>\n

g l\u00e0 gia t\u1ed1c tr\u1ecdng tr\u01b0\u1eddng.<\/p>\n

ch\u1ee9ng minh r\u1eb1ng v\u1edbi m\u1ecdi \u03b1 \u2208(0;\u03c0\/2) \u03b3 \u03b1 lu\u00f4n ti\u1ebfp x\u00fac v\u1edbi parabol (C) c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0<\/p>\n

\"\"<\/p>\n

v\u00e0 t\u00ecm t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m (C) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 parabol an to\u00e0n.<\/p>\n

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

\"\"<\/p>\n

T\u1ecda \u0111\u1ed9 \u0111i\u1ec3m M c\u1ee7a M c\u1ee7a (\u03b3 \u03b1) v\u00e0 (C) l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh sau:<\/p>\n

\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

B\u00e0i 57 (trang 55 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao): a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 \u0111\u1ed3 th\u1ecb (C) h\u00e0m s\u1ed1: f(x)=2×3+3×2+1 b) T\u00ecm c\u00e1c giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng cong (C) v\u00e0 parapol g(x) = 2×2+1 (P) c) Vi\u1ebft Ph\u01b0\u01a1ng tr\u00ecnh c\u00e1c ti\u1ebfp \u0111i\u1ec3m c\u1ee7a (C) v\u00e0 (P) t\u1ea1i c\u00e1c \u0111i\u1ec3m c\u1ee7a ch\u00fang. d) […]<\/p>\n","protected":false},"author":3,"featured_media":23704,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1302],"tags":[1392,1393],"yoast_head":"\n\u0110\u1ea1i s\u1ed1 - Ch\u01b0\u01a1ng 1 - B\u00e0i 8: M\u1ed9t s\u1ed1 b\u00e0i to\u00e1n th\u01b0\u1eddng g\u1eb7p v\u1ec1 \u0111\u1ed3 th\u1ecb<\/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\/dai-so-chuong-1-bai-8-mot-so-bai-toan-thuong-gap-ve-do-thi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0110\u1ea1i s\u1ed1 - Ch\u01b0\u01a1ng 1 - B\u00e0i 8: M\u1ed9t s\u1ed1 b\u00e0i to\u00e1n th\u01b0\u1eddng g\u1eb7p v\u1ec1 \u0111\u1ed3 th\u1ecb\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 57 (trang 55 sgk Gi\u1ea3i T\u00edch 12 n\u00e2ng cao): a) Kh\u1ea3o s\u00e1t s\u1ef1 bi\u1ebfn thi\u00ean v\u00e0 \u0111\u1ed3 th\u1ecb (C) h\u00e0m s\u1ed1: f(x)=2x3+3x2+1 b) T\u00ecm c\u00e1c giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng cong (C) v\u00e0 parapol g(x) = 2x2+1 (P) c) Vi\u1ebft Ph\u01b0\u01a1ng tr\u00ecnh c\u00e1c ti\u1ebfp \u0111i\u1ec3m c\u1ee7a (C) v\u00e0 (P) t\u1ea1i c\u00e1c \u0111i\u1ec3m c\u1ee7a ch\u00fang. d) […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/lop12.edu.vn\/dai-so-chuong-1-bai-8-mot-so-bai-toan-thuong-gap-ve-do-thi\/\" \/>\n<meta property=\"og:site_name\" content=\"Lop12.edu.vn - C\u1ed9ng \u0111\u1ed3ng h\u1ecdc sinh l\u1edbp 12 l\u1edbn nh\u1ea5t t\u1ea1i Vi\u1ec7t Nam\" \/>\n<meta property=\"article:published_time\" content=\"2018-03-26T11:22:34+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/lop12.edu.vn\/wp-content\/uploads\/2018\/03\/1-502.png\" \/>\n\t<meta property=\"og:image:width\" content=\"324\" \/>\n\t<meta property=\"og:image:height\" content=\"67\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"H\u00e0 Trang\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"H\u00e0 Trang\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/lop12.edu.vn\/dai-so-chuong-1-bai-8-mot-so-bai-toan-thuong-gap-ve-do-thi\/\",\"url\":\"https:\/\/lop12.edu.vn\/dai-so-chuong-1-bai-8-mot-so-bai-toan-thuong-gap-ve-do-thi\/\",\"name\":\"\u0110\u1ea1i s\u1ed1 - 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