Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
Trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n<\/a> h\u1ecdc l\u1edbp 9, c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn l\u00e0 ki\u1ebfn th\u1ee9c b\u1eaft bu\u1ed9c c\u1ea7n ph\u1ea3i n\u1eafm v\u1eefng \u0111\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c c\u00e1c d\u1ea1ng to\u00e1n kh\u00f3 v\u00e0 quan tr\u1ecdng. \u0110\u1ec3 h\u1ec7 th\u1ed1ng h\u00f3a l\u1ea1i ki\u1ebfn th\u1ee9c c\u0169ng nh\u01b0 n\u1eafm \u0111\u01b0\u1ee3c c\u00e1c m\u1eb9o \u00f4n luy\u1ec7n n\u00e2ng cao \u0111i\u1ec3m to\u00e1n hi\u1ec7u qu\u1ea3. H\u00e3y c\u00f9ng https::\/\/toppy.vn\/ t\u00ecm hi\u1ec3u qua b\u00e0i gi\u1ea3ng chi ti\u1ebft ngay sau \u0111\u00e2y.<\/p>\n\n\n\n I. L\u00fd thuy\u1ebft v\u1ec1 c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn<\/p>\n\n\n\n X\u00e9t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai m\u1ed9t \u1ea9n ax\u00b2 + bx + c = 0 (Trong \u0111\u00f3 a \u22600), b = 2b\u2019 v\u00e0 \u0394\u2019 = b\u2019\u00b2 \u2013 ac<\/p>\n\n\n\n N\u1ebfu \u0394\u2019 > 0 th\u00ec \u0111\u1ed1i v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai \u0111\u00e3 cho s\u1ebd c\u00f3 hai nghi\u1ec7m ph\u00e2n bi\u1ec7t l\u00e0<\/p>\n\n\n\n x\u2081 = v\u00e0 x\u2082 =<\/p>\n\n\n\n N\u1ebfu \u0394\u2019 = 0 th\u00ec \u0111\u1ed1i v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai \u0111\u00e3 cho s\u1ebd c\u00f3 nghi\u1ec7m k\u00e9p l\u00e0 x\u2081 = x\u2082 =<\/p>\n\n\n\n N\u1ebfu \u0394\u2019 < 0 th\u00ec \u0111\u1ed1i v\u1edbi ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai \u0111\u00e3 cho s\u1ebd v\u00f4 nghi\u1ec7m.<\/p>\n\n\n\n B\u00e0i 5 c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 l\u1edbp 9<\/p>\n\n\n\n Tr\u00ean \u0111\u00e2y l\u00e0 nh\u1eefng ki\u1ebfn th\u1ee9c l\u00fd thuy\u1ebft c\u01a1 b\u1ea3n v\u1ec1 c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 c\u1ea7n n\u1eafm v\u1eefng \u0111\u1ec3 c\u00f3 th\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c c\u00e1c d\u1ea1ng to\u00e1n kh\u00f3 v\u00e0 quan tr\u1ecdng. Tuy nhi\u00ean tr\u01b0\u1edbc khi \u0111i s\u00e2u v\u00e0o c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp c\u1ee7a c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn c\u1ea7n l\u01b0u \u00fd m\u1ed9t s\u1ed1 v\u1ea5n \u0111\u1ec1 sau.<\/p>\n\n\n\n \u0110\u1ed1i v\u1edbi ki\u1ebfn th\u1ee9c c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn l\u1edbp 9, khi \u00e1p d\u1ee5ng c\u1ea7n l\u01b0u \u00fd m\u1ed9t s\u1ed1 v\u1ea5n \u0111\u1ec1 sau:<\/p>\n\n\n\n N\u1ebfu ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai m\u1ed9t \u1ea9n ax\u00b2 + bx + c = 0 v\u00f4 nghi\u1ec7m v\u00e0 a > 0 th\u00ec v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a x, bi\u1ec3u th\u1ee9c ax\u00b2 + bx + c s\u1ebd lu\u00f4n l\u1edbn h\u01a1n 0.<\/p>\n\n\n\n N\u1ebfu ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai m\u1ed9t \u1ea9n ax\u00b2 + bx + c = 0 c\u00f3 h\u1ec7 s\u1ed1 a < 0 n\u00ean th\u1ef1c hi\u1ec7n \u0111\u1ed5i d\u1ea5u 2 v\u1ebf c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y \u0111\u1ec3 h\u1ec7 s\u1ed1 a > 0 \u0111\u1ec3 th\u1ef1c hi\u1ec7n gi\u1ea3i \u0111\u01b0\u1ee3c d\u1ec5 d\u00e0ng h\u01a1n.<\/p>\n\n\n\n \u0110\u1ed1i v\u1edbi nh\u1eefng ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai m\u1ed9t \u1ea9n d\u1ea1ng khuy\u1ebfn nh\u01b0 ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai ax\u00b2 + c = 0 hay ax\u00b2 + bx = 0 ta n\u00ean \u00e1p d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i tr\u1ef1c ti\u1ebfp \u0111\u1ec3 b\u00e0i to\u00e1n \u0111\u01b0\u1ee3c nhanh v\u00e0 ng\u1eafn g\u1ecdn h\u01a1n.<\/p>\n\n\n\n Tr\u00ean \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 l\u01b0u \u00fd v\u1ec1 d\u1ea1ng ki\u1ebfn th\u1ee9c n\u00e0y, c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> c\u1ea7n bi\u1ebft khi \u00e1p d\u1ee5ng. B\u00ean c\u1ea1nh \u0111\u00f3 \u0111\u1ec3 h\u1ec7 th\u1ed1ng h\u00f3a l\u1ea1i ki\u1ebfn th\u1ee9c l\u00fd thuy\u1ebft tr\u1ecdng t\u00e2m l\u1edbp 9 n\u00e0y, d\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n th\u00f4ng d\u1ee5ng gi\u00fap c\u00e1c em d\u1ec5 d\u00e0ng \u00f4n t\u1eadp.<\/p>\n\n\n\n M\u1ed9t s\u1ed1 l\u01b0u \u00fd khi gi\u1ea3i b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn ki\u1ebfn th\u1ee9c n\u00e0y<\/p>\n\n\n\n II. C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp v\u1ec1 c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn<\/p>\n\n\n\n Trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n<\/a> h\u1ecdc c\u1ee7a l\u1edbp 9, c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn l\u00e0 m\u1ed9t trong nh\u1eefng ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng v\u00f4 c\u00f9ng quan tr\u1ecdng \u0111\u1ec3 \u1ee9ng d\u1ee5ng gi\u1ea3i nh\u1eefng d\u1ea1ng to\u00e1n c\u01a1 b\u1ea3n v\u00e0 kh\u00f3. \u0110\u1eb7c bi\u1ec7t l\u00e0 lu\u00f4n \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng trong ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n<\/a> v\u1ec1 sau. Ch\u00ednh v\u00ec v\u1eady \u0111\u1ec3 c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> n\u1eafm v\u1eefng \u0111\u01b0\u1ee3c ki\u1ebfn th\u1ee9c v\u1ec1 c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2 l\u1edbp 9. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n th\u00f4ng d\u1ee5ng th\u01b0\u1eddng g\u1eb7p \u0111\u1ec3 c\u00e1c b\u1ea1n \u00f4n luy\u1ec7n \u0111\u01b0\u1ee3c hi\u1ec7u qu\u1ea3 nh\u1ea5t c\u00f3 th\u1ec3.<\/p>\n\n\n\n C\u00f4ng th\u1ee9c nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc 2<\/p><\/blockquote>\n\n\n\n B\u00e0i t\u1eadp 1 (B\u00e0i 17\/SGK trang 49, To\u00e1n 9, t\u1eadp 2)<\/p>\n\n\n\n X\u00e1c \u0111\u1ecbnh a, b\u2019, c sau \u0111\u00f3 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn \u0111\u1ec3 gi\u1ea3i nh\u1eefng ph\u01b0\u01a1ng tr\u00ecnh d\u01b0\u1edbi \u0111\u00e2y:<\/p>\n\n\n\n C\u00e2u a: 4x\u00b2 + 4x + 1 = 0<\/p>\n\n\n\n C\u00e2u b: 13852x\u00b2 \u2013 14x + 1 = 0<\/p>\n\n\n\n C\u00e2u c: 8x\u00b2 \u2013 x + 1 = 0<\/p>\n\n\n\n C\u00e2u d: 25x\u00b2 + 10x + 1 = 0<\/p>\n\n\n\n B\u00e0i t\u1eadp 2 (B\u00e0i 18\/SGK trang 49, To\u00e1n 9, t\u1eadp 2)<\/p>\n\n\n\n \u0110\u01b0a nh\u1eefng ph\u01b0\u01a1ng tr\u00ecnh d\u01b0\u1edbi \u0111\u00e2y v\u1ec1 d\u1ea1ng sau: ax2 + 2b\u2019x + c = 0, sau \u0111\u00f3 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh. S\u1eed d\u1ee5ng b\u1ea3ng s\u1ed1 hay m\u00e1y t\u00ednh \u0111\u1ec3 vi\u1ebft nghi\u1ec7m t\u00ecm \u0111\u01b0\u1ee3c g\u1ea7n \u0111\u00fang nh\u1ea5t (l\u01b0u \u00fd, l\u00e0m tr\u00f2n k\u1ebft qu\u1ea3 \u1edf ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 2):<\/p>\n\n\n\n C\u00e2u a: 3x\u00b2 \u2013 2x = x\u00b2 + 3<\/p>\n\n\n\n C\u00e2u b: (2x \u2013 \u221a2)\u00b2x \u2013 1 = (x + 1)(x \u2013 1)<\/p>\n\n\n\n C\u00e2u c: 3x\u00b2 + 3 = 2(x + 1)<\/p>\n\n\n\n C\u00e2u d: 0,5x(x + 1) = (x \u2013 1)\u00b2<\/p>\n\n\n\n B\u00e0i t\u1eadp 3 (B\u00e0i 19\/SGK trang 49, To\u00e1n 9, t\u1eadp 2)<\/p>\n\n\n\n \u0110\u1ed1: \u0110\u1ed1 c\u00e1c em bi\u1ebft t\u1ea1i sao khi a > 0, ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai m\u1ed9t \u1ea9n ax\u00b2 + bx + c = 0 (Trong \u0111\u00f3 a \u22600) v\u00f4 nghi\u1ec7m th\u00ec v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb c\u1ee7a x ta lu\u00f4n c\u00f3 ax\u00b2 + bx + c > 0.<\/p>\n\n\n\n C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp th\u00f4ng d\u1ee5ng v\u1ec1 c\u00f4ng th\u1ee9c c\u1ee7a nghi\u1ec7m thu g\u1ecdn<\/p>\n\n\n\n B\u00e0i t\u1eadp 4 (B\u00e0i 20\/SGK trang 49, To\u00e1n 9, t\u1eadp 2)<\/p>\n\n\n\n \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn \u0111\u1ec3 gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc hai sau:<\/p>\n\n\n\n C\u00e2u a: 25x\u00b2 \u2013 16 = 0<\/p>\n\n\n\n C\u00e2u b: 2x\u00b2 + 3 = 0<\/p>\n\n\n\n C\u00e2u c: 4.2x\u00b2 + 5,46x = 0<\/p>\n\n\n\n C\u00e2u d: 4x\u00b2 \u2013 2\u221a3x = 1 \u2013 \u221a3<\/p>\n\n\n\n B\u00e0i t\u1eadp 5 (B\u00e0i 21\/SGK trang 49, To\u00e1n 9, t\u1eadp 2)<\/p>\n\n\n\n Gi\u1ea3i c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a \u00f4ng An Kh\u00f4-va-ri-zmi d\u1ef1a v\u00e0o l\u00fd thuy\u1ebft c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn \u0111\u00e3 h\u1ecdc:<\/p>\n\n\n\n C\u00e2u a: x\u00b2 = 12x + 228<\/p>\n\n\n\n C\u00e2u b: = 19<\/p>\n\n\n\n B\u00e0i gi\u1ea3ng tr\u00ean \u0111\u00e3 cung c\u1ea5p cho c\u00e1c b\u1ea1n ki\u1ebfn th\u1ee9c l\u00fd thuy\u1ebft v\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp th\u00f4ng d\u1ee5ng v\u1ec1 c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn l\u1edbp 9. Hy v\u1ecdng nh\u1eefng ki\u1ebfn th\u1ee9c tr\u00ean \u0111\u00e2y s\u1ebd l\u00e0 n\u1ed9i dung b\u1ed5 \u00edch d\u00e0nh cho c\u00e1c b\u1ea1n h\u1ecdc sinh v\u00e0 c\u00e1c b\u1eadc ph\u1ee5 huynh c\u00f3 nhu c\u1ea7u \u00f4n t\u1eadp v\u00e0 gi\u1ea3ng d\u1ea1y cho c\u00e1c em. Ngo\u00e0i ra trong qu\u00e1 tr\u00ecnh h\u1ecdc t\u1eadp v\u00e0 \u00f4n luy\u1ec7n, n\u1ebfu c\u00f3 nhu c\u1ea7u t\u00ecm ki\u1ebfm \u0111\u01a1n v\u1ecb h\u1ecdc t\u1eadp<\/a> uy t\u00edn, ch\u1ea5t l\u01b0\u1ee3ng ho\u1eb7c mu\u1ed1n \u0111\u01b0\u1ee3c gi\u1ea3i \u0111\u00e1p v\u1ec1 nh\u1eefng ki\u1ebfn th\u1ee9c li\u00ean quan \u0111\u1ebfn m\u00f4n h\u1ecdc, h\u00e3y li\u00ean h\u1ec7 v\u1edbi Vietlearn.org\/ ch\u00fang t\u00f4i \u0111\u1ec3 \u0111\u01b0\u1ee3c gi\u1ea3i \u0111\u00e1p s\u1edbm nh\u1ea5t c\u00f3 th\u1ec3.<\/p>\n\n\n\n T\u00ecm hi\u1ec3u th\u00eam:<\/p>\n\n\n\n H\u1ec7 th\u1ee9c Vi-\u00e9t v\u00e0 \u1ee9ng d\u1ee5n<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn Trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n h\u1ecdc l\u1edbp 9, c\u00f4ng th\u1ee9c nghi\u1ec7m thu g\u1ecdn l\u00e0 ki\u1ebfn th\u1ee9c b\u1eaft bu\u1ed9c c\u1ea7n ph\u1ea3i n\u1eafm v\u1eefng \u0111\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c c\u00e1c d\u1ea1ng to\u00e1n kh\u00f3 v\u00e0 quan tr\u1ecdng. \u0110\u1ec3 h\u1ec7 th\u1ed1ng h\u00f3a l\u1ea1i ki\u1ebfn th\u1ee9c c\u0169ng nh\u01b0 n\u1eafm \u0111\u01b0\u1ee3c c\u00e1c m\u1eb9o \u00f4n luy\u1ec7n n\u00e2ng cao \u0111i\u1ec3m […]<\/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],"tags":[],"class_list":["post-989","post","type-post","status-publish","format-standard","hentry","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/989","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=989"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/989\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=989"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=989"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=989"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}