Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
To\u00e1n h\u1ecdc l\u00e0 m\u1ed9t m\u00f4n h\u1ecdc v\u00f4 c\u00f9ng quan tr\u1ecdng, n\u00f3 kh\u00f4ng ch\u1ec9 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng t\u1ea1i tr\u01b0\u1eddng h\u1ecdc m\u00e0 n\u00f3 c\u00f2n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ea5t ph\u1ed5 bi\u1ebfn trong cu\u1ed9c s\u1ed1ng h\u1eb1ng ng\u00e0y. H\u00f4m nay, Vietlearn s\u1ebd gi\u1edbi thi\u1ec7u \u0111\u1ebfn cho c\u00e1c b\u1ea1n m\u1ed9t d\u1ea1ng to\u00e1n c\u01a1 b\u1ea3n nh\u01b0ng l\u1ea1i r\u1ea5t quan tr\u1ecdng \u0111\u00f3 l\u00e0 d\u1ea1ng b\u00e0i r\u00fat g\u1ecdn ph\u00e2n th\u1ee9c. C\u00f9ng ch\u00fang t\u00f4i kh\u00e1m ph\u00e1 to\u00e1n 8 r\u00fat g\u1ecdn ph\u00e2n th\u1ee9c ngay sau \u0111\u00e2y nh\u00e9!<\/p>\n\n\n\n
C\u00e1ch r\u00fat g\u1ecdn ph\u00e2n th\u1ee9c \u0111\u1ea1i s\u1ed1 l\u1edbp 8<\/p>\n\n\n\n
T\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n th\u1ee9c<\/p>\n\n\n\n
T\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n th\u1ee9c to\u00e1n 8: \u0110\u00e2y l\u00e0 nh\u1eefng t\u00ednh ch\u1ea5t quan tr\u1ecdng y\u00eau c\u1ea7u c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> ph\u1ea3i h\u1ecdc thu\u1ed9c \u0111\u1ec3 c\u00f3 th\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c nh\u1eefng d\u1ea1ng b\u00e0i t\u1eadp ph\u00e2n th\u1ee9c.<\/p>\n\n\n\n A\/B = A.M\/B.M v\u1edbi \u0111i\u1ec1u ki\u1ec7n M l\u00e0 m\u1ed9t \u0111a th\u1ee9c kh\u00e1c 0<\/p>\n\n\n\n A\/B = A:N\/B:N v\u1edbi \u0111i\u1ec1u ki\u1ec7n N l\u00e0 m\u1ed9t \u0111a th\u1ee9c kh\u00e1c kh\u00f4ng, trong ph\u00e9p t\u00ednh n\u00e0y N \u0111\u01b0\u1ee3c coi l\u00e0 nh\u00e2n t\u1eed chung c\u1ee7a ph\u00e2n th\u1ee9c<\/p>\n\n\n\n Quy t\u1eafc \u0111\u1ed5i d\u1ea5u m\u00e0 h\u1ecdc sinh<\/a> n\u00ean nh\u1edb:<\/p>\n\n\n\n \u0110\u1ed5i d\u1ea5u ph\u00e2n th\u1ee9c v\u00e0 t\u1eed s\u1ed1: A\/B = -(-A)\/B<\/p>\n\n\n\n \u0110\u1ed5i d\u1ea5u ph\u00e2n th\u1ee9c v\u00e0 m\u1eabu s\u1ed1: A\/B = -(A)\/-B<\/p>\n\n\n\n \u0110\u1ed5i d\u1ea5u m\u1eabu: A\/-B = -(A)\/B<\/p>\n\n\n\n N\u1ebfu \u0111\u1ed5i d\u1ea5u t\u1eed v\u00e0 m\u1eabu c\u1ee7a m\u1ed9t ph\u00e2n th\u1ee9c ta s\u1ebd \u0111\u01b0\u1ee3c m\u1ed9t ph\u00e2n th\u1ee9c m\u1edbi b\u1eb1ng v\u1edbi ph\u00e2n th\u1ee9c \u0111\u00e3 cho: A\/B = -A\/-B<\/p>\n\n\n\n Ph\u00e2n th\u1ee9c \u0111\u1ea1i s\u1ed1<\/p><\/blockquote>\n\n\n\n L\u00fd do c\u1ea7n l\u00e0m c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp r\u00fat g\u1ecdn ph\u00e2n th\u1ee9c l\u1edbp 8<\/p>\n\n\n\n T\u0103ng t\u01b0 duy logic<\/p>\n\n\n\n R\u00fat g\u1ecdn ph\u00e2n th\u1ee9c \u0111\u1ea1i s\u1ed1 l\u1edbp 8 \u0111\u01b0\u1ee3c xem l\u00e0 d\u1ea1ng b\u00e0i t\u1eadp \u0111\u01a1n gi\u1ea3n, kh\u00f4ng qu\u00e1 kh\u00f3 ch\u1ec9 c\u1ea7n h\u1ecdc sinh<\/a> t\u1eadp trung khi l\u00e0m th\u00ec k\u1ebft qu\u1ea3 s\u1ebd r\u1ea5t t\u1ed1t. \u0110\u00e2y l\u00e0 d\u1ea1ng b\u00e0i t\u1eadp c\u01a1 b\u1ea3n gi\u00fap h\u1ecdc sinh<\/a> c\u00f3 th\u1ec3 h\u00ecnh dung v\u00e0 t\u01b0 duy, Nh\u1edd v\u1eady, sau n\u00e0y c\u00f3 th\u1ec3 h\u1ecdc t\u1ed1t v\u00e0 l\u00e0m \u0111\u01b0\u1ee3c nh\u1eefng d\u1ea1ng b\u00e0i t\u1eadp kh\u00f3 h\u01a1n, y\u00eau c\u1ea7u kh\u1ea3 n\u0103ng t\u01b0 duy v\u00e0 ph\u00e2n t\u00edch v\u00f4 c\u00f9ng cao.<\/p>\n\n\n\n Tuy nhi\u00ean, r\u1ea5t nhi\u1ec1u b\u1ea1n h\u1ecdc sinh<\/a> ch\u1ee7 quan cho r\u1eb1ng r\u00fat g\u1ecdn c\u00e1c ph\u00e2n th\u1ee9c l\u00e0 nh\u1eefng c\u00e2u b\u00e0i t\u1eadp \u0111\u01a1n gi\u1ea3n. V\u00ec v\u1eady kh\u00f4ng t\u1eadp trung v\u00e0o vi\u1ec7c h\u1ecdc, ph\u00e2n t\u00edch c\u00e1ch gi\u1ea3i m\u00e0 ch\u1ec9 l\u00e0m qua loa \u0111\u1ec3 cho xong. Vi\u1ec7c \u0111\u00f3 d\u1eabn \u0111\u1ebfn t\u00ednh tr\u1ea1ng k\u1ebft qu\u1ea3 h\u1ecdc t\u1eadp<\/a> ng\u00e0y c\u00e0ng sa s\u00fat. Nh\u01b0 v\u1eady, c\u00f3 th\u1ec3 th\u1ea5y c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp n\u00e0y ch\u00ednh l\u00e0 ti\u1ec1n \u0111\u1ec1 \u0111\u1ec3 cho h\u1ecdc sinh<\/a> c\u00f3 th\u1ec3 ph\u00e1t tri\u1ec3n t\u01b0 duy v\u00e0 kh\u1ea3 n\u0103ng ph\u00e2n t\u00edch cho nh\u1eefng d\u1ea1ng b\u00e0i t\u1eadp ph\u00e2n th\u1ee9c kh\u00f3 h\u01a1n.<\/p>\n\n\n\n \u1ee8ng d\u1ee5ng t\u1ed1t h\u01a1n trong c\u00e1c m\u00f4n h\u1ecdc kh\u00e1c<\/p>\n\n\n\n Ngo\u00e0i ra, c\u00e1ch r\u00fat g\u1ecdn c\u00e1c ph\u00e2n th\u1ee9c kh\u00f4ng ch\u1ec9 \u00e1p d\u1ee5ng cho ri\u00eang m\u00f4n to\u00e1n. C\u00e1ch r\u00fat g\u1ecdn n\u00e0y c\u00f2n th\u01b0\u1eddng xuy\u00ean \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong m\u00f4n h\u00f3a h\u1ecdc, m\u00f4n l\u00fd, m\u00f4n sinh h\u1ecdc,\u2026 v\u00e0 c\u00e1c c\u00e2u t\u00ednh to\u00e1n \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng t\u1ea1i c\u00e1c tr\u01b0\u1eddng \u0111\u1ea1i h\u1ecdc. V\u00ec v\u1eady, vi\u1ec7c h\u1ecdc t\u1ed1t v\u00e0 l\u00e0m t\u1ed1t c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp v\u1ec1 vi\u1ec7c l\u00e0m g\u1ecdn ph\u00e2n th\u1ee9c \u0111\u1ea1i s\u1ed1 s\u1ebd gi\u00fap cho h\u1ecdc sinh d\u1ec5 d\u00e0ng chinh ph\u1ee5c nh\u1eefng c\u1ed9t m\u1ed1c quan tr\u1ecdng h\u01a1n trong t\u01b0\u01a1ng lai.<\/p>\n\n\n\n B\u00e0i t\u1eadp r\u00fat g\u1ecdn s\u1ebd gi\u00fap h\u1ecdc sinh ph\u00e1t tri\u1ec3n \u0111\u01b0\u1ee3c kh\u1ea3 n\u0103ng ph\u00e2n t\u00edch<\/p>\n\n\n\n Do \u0111\u00f3, \u0111\u00e2y l\u00e0 d\u1ea1ng b\u00e0i t\u1eadp v\u00f4 c\u00f9ng quan tr\u1ecdng m\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh c\u1ea7n l\u01b0u \u00fd \u0111\u1ec3 c\u00f3 ph\u00e1t tri\u1ec3n con \u0111\u01b0\u1eddng h\u1ecdc v\u1ea5n c\u1ee7a b\u1ea3n th\u00e2n. V\u00e0 c\u00e1ch duy nh\u1ea5t \u0111\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c \u0111i\u1ec1u \u0111\u00f3 l\u00e0 ph\u1ea3i lu\u00f4n t\u1eadp trung cao \u0111\u1ed9 khi gi\u1ea3i nh\u1eefng b\u00e0i to\u00e1n r\u00fat g\u1ecdn \u0111\u1ec3 c\u00f3 th\u1ec3 t\u01b0 duy v\u00e0 ph\u00e1t tri\u1ec3n m\u1ed9t c\u00e1ch nhanh ch\u00f3ng v\u00e0 to\u00e0n di\u1ec7n h\u01a1n.<\/p>\n\n\n\n R\u00fat g\u1ecdn ph\u00e2n th\u1ee9c \u0111\u1ea1i s\u1ed1<\/p>\n\n\n\n R\u00fat g\u1ecdn ph\u00e2n th\u1ee9c l\u00e0 d\u1ea1ng b\u00e0i c\u01a1 b\u1ea3n tuy nhi\u00ean mu\u1ed1n l\u00e0m t\u1ed1t th\u00ec h\u1ecdc c\u1ea7n ph\u1ea3i c\u00f3 kh\u1ea3 n\u0103ng ph\u00e2n t\u00edch b\u00e0i to\u00e1n nhanh nh\u1ea1y. D\u1ea1ng b\u00e0i l\u00e0m g\u1ecdn c\u00e1c \u0111\u1ea1i s\u1ed1 ch\u00ednh l\u00e0 c\u00e1ch bi\u1ebfn \u0111\u1ed5i nh\u1eefng ph\u00e2n th\u1ee9c ph\u1ee9c t\u1ea1p th\u00e0nh nh\u1eefng ph\u00e2n th\u1ee9c \u0111\u01a1n gi\u1ea3n h\u01a1n v\u00e0 b\u1eb1ng v\u1edbi ph\u00e2n th\u1ee9c \u0111a cho.<\/p>\n\n\n\n Mu\u1ed1n th\u1ef1c hi\u1ec7n m\u1ed9t c\u00e1ch nhanh ch\u00f3ng, ch\u00ednh x\u00e1c ta c\u00f3 th\u1ec3 l\u00e0m nh\u01b0 sau:<\/p>\n\n\n\n Ph\u00e2n t\u00edch t\u1eed v\u00e0 m\u1eabu th\u00e0nh nh\u1eefng nh\u00e2n t\u1eed \u0111\u1ec3 c\u00f3 th\u1ec3 t\u00ecm \u0111\u01b0\u1ee3c nh\u00e2n t\u1eed chung.<\/p>\n\n\n\n Chia c\u1ea3 t\u1eed v\u00e0 m\u1eabu cho nh\u00e2n t\u1eed chung \u0111\u1ec3 r\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c<\/p>\n\n\n\n V\u00ed d\u1ee5: R\u00fat g\u1ecdn ph\u00e2n th\u1ee9c sau A = (x + 3×2)\/( x2 \u2013 2x)<\/p>\n\n\n\n B\u01b0\u1edbc 1: Ph\u00e2n t\u00edch t\u1eed v\u00e0 m\u1eabu \u0111\u1ec3 t\u00ecm nh\u00e2n t\u1eed chung<\/p>\n\n\n\n A = x(1 + 3x)\/x(x \u2013 2)<\/p>\n\n\n\n V\u1eady ta c\u00f3 nh\u00e2n t\u1eed chung l\u00e0 x<\/p>\n\n\n\n B\u01b0\u1edbc 2: Chia c\u1ea3 t\u1eed v\u00e0 m\u1eabu cho nh\u00e2n t\u1eed chung x<\/p>\n\n\n\n V\u1eady ta \u0111\u01b0\u1ee3c ph\u00e2n th\u1ee9c r\u00fat g\u1ecdn b = (1 + 3x)\/(x \u2013 2) b\u1eb1ng v\u1edbi ph\u00e2n th\u1ee9c A = (x + 3×2)\/( x2 \u2013 2x)<\/p>\n\n\n\n B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng<\/p>\n\n\n\n B\u00e0i t\u1eadp th\u1ef1c h\u00e0nh<\/p>\n\n\n\n B\u00e0i 1: R\u00fat g\u1ecdn ph\u00e2n th\u1ee9c sau A = x(2y \u2013 5) + xy +5x<\/p>\n\n\n\n Gi\u1ea3i:<\/p>\n\n\n\n A = x(2y \u2013 5) + xy +5x<\/p>\n\n\n\n A = 3xy<\/p>\n\n\n\n B\u00e0i 2: C\u00e1c nh\u1eadn \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y \u0111\u00fang hay sai?<\/p>\n\n\n\n 3xy\/9y = x\/3<\/p>\n\n\n\n (3xy + 3)\/(9y + 3) = x\/3<\/p>\n\n\n\n (3xy + 3)\/(9y + 3) = (x + 1)\/6<\/p>\n\n\n\n (3xy + 3)\/(9y + 9) = x\/3<\/p>\n\n\n\n Gi\u1ea3i:<\/p>\n\n\n\n a) \u0110\u00fang v\u00ec \u0111\u00e3 chia c\u1ea3 t\u1eed c\u1ea3 m\u1eabu c\u1ee7a v\u1ebf tr\u00e1i cho 3y.<\/p>\n\n\n\n b) V\u1ebf ph\u1ea3i ch\u1ee9ng t\u1ecf \u0111\u00e3 chia m\u1eabu c\u1ee7a v\u1ebf tr\u00e1i cho 3y + 1 v\u00ec 9y + 3 = 3(3y + 1)<\/p>\n\n\n\n Nh\u01b0ng t\u1eed c\u1ee7a v\u1ebf tr\u00e1i kh\u00f4ng c\u00f3 nh\u00e2n t\u1eed 3y + 1. N\u00ean ph\u00e9p r\u00fat g\u1ecdn n\u00e0y sai.<\/p>\n\n\n\n c) Sai, v\u00ec y kh\u00f4ng ph\u1ea3i l\u00e0 nh\u00e2n t\u1eed chung c\u1ee7a t\u1eed th\u1ee9c v\u00e0 m\u1eabu th\u1ee9c c\u1ee7a v\u1ebf tr\u00e1i<\/p>\n\n\n\n d) \u0110\u00fang, v\u00ec \u0111\u00e3 r\u00fat g\u1ecdn ph\u00e2n th\u1ee9c \u1edf v\u1ebf tr\u00e1i v\u1edbi nh\u00e2n t\u1eed chung l\u00e0 3(y + 1)<\/p>\n\n\n\n L\u1eddi k\u1ebft<\/p>\n\n\n\n B\u00e0i vi\u1ebft tr\u00ean l\u00e0 m\u1ed9t s\u1ed1 ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n m\u00e0 v\u1ec1 c\u00e1ch t\u00ednh r\u00fat g\u1ecdn ph\u00e2n th\u1ee9c \u0111\u1ea1i s\u1ed1 l\u1edbp 8 m\u00e0 Vietlearn mu\u1ed1n g\u1eedi \u0111\u1ebfn cho c\u00e1c b\u1ea1n h\u1ecdc sinh. Mong r\u1eb1ng, v\u1edbi nh\u1eefng th\u00f4ng tin m\u00e0 b\u00e0i vi\u1ebft cung c\u1ea5p b\u1ea1n s\u1ebd nh\u1eadn ra s\u1ef1 quan tr\u1ecdng c\u1ee7a d\u1ea1ng b\u00e0i t\u1eadp r\u00fat g\u1ecdn ph\u00e2n th\u1ee9c v\u00e0 ch\u0103m ch\u1ec9 h\u1ecdc t\u1eadp h\u01a1n. N\u1ebfu mu\u1ed1n t\u00ecm hi\u1ec3u th\u00eam c\u00e1c d\u1ea1ng to\u00e1n kh\u00e1c, th\u00ec h\u00e3y truy c\u1eadp ngay v\u00e0o website: Vietlearn.org\/ c\u1ee7a Vietlearn \u0111\u1ec3 t\u00ecm hi\u1ec3u nh\u00e9!<\/p>\n\n\n\n <\/p>\n\n\n\n Quy \u0111\u1ed3ng m\u1eabu th\u1ee9c nhi\u1ec1u ph\u00e2n th\u1ee9c l\u1edbp 8 \u2013 H\u1ecdc to\u00e1n c\u00f9ng Vietlearn<\/p>\n\n\n\n Ph\u00e9p nh\u00e2n<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn To\u00e1n h\u1ecdc l\u00e0 m\u1ed9t m\u00f4n h\u1ecdc v\u00f4 c\u00f9ng quan tr\u1ecdng, n\u00f3 kh\u00f4ng ch\u1ec9 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng t\u1ea1i tr\u01b0\u1eddng h\u1ecdc m\u00e0 n\u00f3 c\u00f2n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ea5t ph\u1ed5 bi\u1ebfn trong cu\u1ed9c s\u1ed1ng h\u1eb1ng ng\u00e0y. H\u00f4m nay, Vietlearn s\u1ebd gi\u1edbi thi\u1ec7u \u0111\u1ebfn cho c\u00e1c b\u1ea1n m\u1ed9t d\u1ea1ng to\u00e1n c\u01a1 b\u1ea3n nh\u01b0ng […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9,4],"tags":[],"class_list":["post-1041","post","type-post","status-publish","format-standard","hentry","category-toan-hoc","category-trung-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1041","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=1041"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1041\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=1041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=1041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=1041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}= 2xy -5x +xy +5x\n\n= 2xy + xy +5x \u2013 5x<\/code><\/pre>\n\n\n\n