{"id":1109,"date":"2021-10-08T13:15:19","date_gmt":"2021-10-08T13:15:19","guid":{"rendered":"https:\/\/www.vietlearn.org\/post\/?p=1109"},"modified":"2021-10-14T22:11:31","modified_gmt":"2021-10-14T15:11:31","slug":"can-bac-hai-lop-9-khai-niem-va-cac-dinh-ly-lien-quan","status":"publish","type":"post","link":"https:\/\/www.vietlearn.org\/kien-thuc\/can-bac-hai-lop-9-khai-niem-va-cac-dinh-ly-lien-quan\/","title":{"rendered":"C\u0103n b\u1eadc hai l\u1edbp 9 \u2013 Kh\u00e1i ni\u1ec7m v\u00e0 c\u00e1c \u0111\u1ecbnh l\u00fd li\u00ean quan"},"content":{"rendered":"\n

Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n

Trong to\u00e1n h\u1ecdc, c\u0103n b\u1eadc 2 l\u00e0 ph\u1ea7n ki\u1ebfn th\u1ee9c tr\u1ecdng y\u1ebfu, b\u1ea1n b\u1eaft bu\u1ed9c ph\u1ea3i n\u1eafm \u0111\u01b0\u1ee3c nh\u1eefng ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n<\/a> v\u1ec1 m\u1ea3ng n\u00e0y \u0111\u1ec3 tr\u00e1nh g\u1eb7p ph\u1ea3i nh\u1eefng sai s\u00f3t kh\u00f4ng \u0111\u00e1ng. Tuy nhi\u00ean, n\u1ebfu \u0111\u1ec3 h\u1ecdc m\u1ed9t l\u1ea7n h\u1ebft t\u1ea5t c\u1ea3 c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 c\u0103n b\u1eadc 2 l\u00e0 \u0111i\u1ec1u kh\u00f4ng kh\u1ea3 thi. V\u1eady n\u00ean, ph\u1ea7n ki\u1ebfn th\u1ee9c n\u00e0y \u0111\u01b0\u1ee3c n\u00e2ng c\u1ea5p d\u1ea7n d\u1ea7n qua c\u00e1c n\u0103m h\u1ecdc. B\u1ea1n \u0111\u00e3 h\u1ecdc \u0111\u01b0\u1ee3c m\u1ed9t v\u00e0i ph\u1ea7n v\u1ec1 c\u0103n b\u1eadc 2 \u1edf l\u1edbp 7 r\u1ed3i, v\u1eady v\u1edbi ph\u1ea7n c\u0103n b\u1eadc hai l\u1edbp 9 n\u00e0y, b\u1ea1n s\u1ebd \u0111\u01b0\u1ee3c b\u1ed5 sung th\u00eam ki\u1ebfn th\u1ee9c g\u00ec?<\/p>\n\n\n\n

Chuy\u00ean \u0111\u1ec1 c\u0103n b\u1eadc hai l\u1edbp 9 \u0111\u1ec1 c\u1eadp t\u1edbi nh\u1eefng lo\u1ea1i c\u0103n b\u1eadc 2 n\u00e0o?<\/p>\n\n\n\n

Nh\u01b0 \u0111\u00e3 \u0111\u1ec1 c\u1eadp qua \u1edf ph\u1ea7n m\u1edf \u0111\u1ea7u, m\u1edbi h\u1ecdc th\u00ec c\u00f3 th\u1ec3 nhi\u1ec1u b\u1ea1n s\u1ebd th\u1ea5y c\u0103n b\u1eadc hai l\u00e0 ph\u00e9p to\u00e1n d\u1ec5, s\u1eed d\u1ee5ng \u0111\u01a1n gi\u1ea3n kh\u00f4ng c\u00f3 g\u00ec kh\u00f3. Nh\u01b0ng th\u1ef1c t\u1ebf, trong nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc th\u00ec l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c v\u1ec1 c\u0103n b\u1eadc hai n\u00e0y c\u1ef1c nhi\u1ec1u, c\u1ef1c r\u1ed9ng m\u00e0 h\u1ebft ch\u01b0\u01a1ng tr\u00ecnh ph\u1ed5 th\u00f4ng ch\u1eafc ch\u1eafn b\u1ea1n c\u0169ng kh\u00f4ng th\u1ec3 bi\u1ebft h\u1ebft \u0111\u01b0\u1ee3c.<\/p>\n\n\n\n

Ph\u1ea7n m\u1edf \u0111\u1ea7u c\u1ee7a c\u0103n b\u1eadc hai l\u1edbp 9 s\u1ebd b\u1ed5 sung cho b\u1ea1n nh\u1eefng ki\u1ebfn th\u1ee9c m\u1edbi g\u00ec?<\/p>\n\n\n\n

Tuy nhi\u00ean, l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c \u0111\u1ed3 s\u1ed9 v\u1ec1 c\u0103n b\u1eadc 2 \u0111\u00f3 kh\u00f4ng y\u00eau c\u1ea7u h\u1ecdc sinh<\/a> ph\u1ea3i n\u1eafm \u0111\u01b0\u1ee3c h\u1ebft. C\u00e1c b\u1ea1n ch\u1ec9 c\u1ea7n h\u1ecdc nh\u1eefng g\u00ec c\u01a1 b\u1ea3n nh\u1ea5t \u0111\u1ec3 ph\u1ee5c v\u1ee5 cho m\u00f4n to\u00e1n h\u1ecdc \u1edf c\u00e1c l\u1edbp tr\u00ean. V\u00e0 c\u1ee5 th\u1ec3 trong ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n<\/a> 9 c\u0103n b\u1eadc hai n\u00e0y, c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> s\u1ebd v\u1eeba \u0111\u01b0\u1ee3c c\u1ee7ng c\u1ed1 l\u1ea1i m\u1ed9t s\u1ed1 ki\u1ebfn th\u1ee9c c\u0169 \u0111\u00e3 h\u1ecdc t\u1eeb n\u0103m l\u1edbp 7.<\/p>\n\n\n\n

To\u00e1n 9 c\u0103n b\u1eadc hai c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c chia th\u00e0nh 2 lo\u1ea1i ph\u1ed5 bi\u1ebfn, g\u1ecdi l\u00e0 c\u0103n b\u1eadc 2 s\u1ed1 h\u1ecdc v\u00e0 c\u0103n th\u1ee9c b\u1eadc 2. Th\u00f4ng th\u01b0\u1eddng, khi g\u1ecdi l\u00e0 \u201cc\u0103n b\u1eadc 2\u201d m\u00e0 kh\u00f4ng th\u00eam g\u00ec th\u00ec ng\u01b0\u1eddi nghe ho\u1eb7c ng\u01b0\u1eddi \u0111\u1ecdc h\u00e3y t\u1ef1 \u0111\u1ed9ng hi\u1ec3u \u0111\u00f3 l\u00e0 \u0111ang nh\u1eafc \u0111\u1ebfn c\u0103n b\u1eadc 2 s\u1ed1 h\u1ecdc. V\u00e0 ph\u1ea7n h\u00f4m nay ch\u00fang ta c\u1ee7ng c\u1ed1 l\u1ea1i c\u0169ng l\u00e0 v\u1ec1 n\u1ed9i dung n\u00e0y.<\/p>\n\n\n\n

\u0110i\u1ec3m l\u1ea1i m\u1ed9t s\u1ed1 ki\u1ebfn th\u1ee9c v\u1ec1 c\u0103n b\u1eadc 2 \u0111\u00e3 \u0111\u01b0\u1ee3c h\u1ecdc \u1edf l\u1edbp 7<\/p>\n\n\n\n

Tr\u01b0\u1edbc khi ti\u1ebfn v\u00e0o n\u1ed9i dung c\u1ee7a ph\u1ea7n c\u0103n b\u1eadc 2 l\u1edbp 9 th\u00ec ch\u00fang ta n\u00ean \u0111i\u1ec3m l\u1ea1i nh\u1eefng ki\u1ebfn th\u1ee9c \u0111\u00e3 \u0111\u01b0\u1ee3c cung c\u1ea5p v\u1ec1 n\u1ed9i dung n\u00e0y \u1edf ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 7<\/a>. Vi\u1ec7c n\u00e0y v\u1eeba gi\u00fap b\u1ea1n c\u1ee7ng c\u1ed1 tr\u00ed nh\u1edb l\u1ea1i v\u1eeba gi\u00fap b\u1ea1n tr\u00e1nh b\u1ecb h\u1ecdc l\u1eb7p ki\u1ebfn th\u1ee9c.<\/p>\n\n\n\n

C\u0103n b\u1eadc hai c\u1ee7a m\u1ed9t s\u1ed1 b\u1ea5t k\u1ef3 \u0111\u00e3 \u0111\u01b0\u1ee3c h\u1ecdc theo ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n<\/a> l\u1edbp 7<\/p>\n\n\n\n

S\u1ed1 \u201cx\u201d \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 c\u0103n b\u1eadc 2 c\u1ee7a m\u1ed9t s\u1ed1 \u201ca\u201d kh\u00f4ng \u00e2m n\u1ebfu x2= a .<\/p>\n\n\n\n

M\u1ed9t s\u1ed1 d\u01b0\u01a1ng \u201ca\u201d (a>0) c\u00f3 \u0111\u00fang 2 c\u0103n b\u1eadc hai. \u0110\u00f3 l\u00e0 2 s\u1ed1 \u221a a v\u00e0 -\u221a a .<\/p>\n\n\n\n

Ri\u00eang s\u1ed1 0 th\u00ec ch\u1ec9 c\u00f3 duy nh\u1ea5t m\u1ed9t c\u0103n b\u1eadc 2 b\u1eb1ng ch\u00ednh n\u00f3, vi\u1ebft l\u00e0: \u221a 0= 0.<\/p>\n\n\n\n

V\u00ed d\u1ee5: v\u1edbi s\u1ed1 36, ta s\u1ebd c\u00f3 2 c\u0103n b\u1eadc hai c\u1ee7a s\u1ed1 n\u00e0y l\u00e0 6 v\u00e0 -6.<\/p>\n\n\n\n

\u0110\u00f3 l\u00e0 nh\u1eefng g\u00ec ph\u1ea7n To\u00e1n 7 \u0111\u00e3 cung c\u1ea5p cho b\u1ea1n. V\u1eady sang t\u1edbi to\u00e1n 9 c\u0103n b\u1eadc hai, ch\u00fang ta s\u1ebd \u0111\u01b0\u1ee3c b\u1ed5 sung th\u00eam ki\u1ebfn th\u1ee9c g\u00ec m\u1edbi? C\u00e2u tr\u1ea3 l\u1eddi l\u00e0 b\u1ea1n s\u1ebd \u0111\u01b0\u1ee3c ho\u00e0n thi\u1ec7n v\u00e0 c\u00f3 m\u1ed9t kh\u00e1i ni\u1ec7m chu\u1ea9n x\u00e1c v\u1ec1 c\u0103n b\u1eadc 2 s\u1ed1 h\u1ecdc. B\u00ean c\u1ea1nh \u0111\u00f3, b\u1ed5 sung \u0111\u1ecbnh l\u00ed so s\u00e1nh v\u1ec1 c\u00e1c c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc n\u00e0y.<\/p>\n\n\n\n

Kh\u00e1i ni\u1ec7m v\u1ec1 c\u0103n b\u1eadc 2 s\u1ed1 h\u1ecdc<\/p>\n\n\n\n

C\u0103n b\u1eadc 2 s\u1ed1 h\u1ecdc c\u1ee7a m\u1ed9t s\u1ed1 d\u01b0\u01a1ng \u201ca\u201d c\u0169ng lu\u00f4n c\u00f3 gi\u00e1 tr\u1ecb d\u01b0\u01a1ng. C\u1ee5 th\u1ec3, nh\u01b0 \u1edf To\u00e1n 7 ch\u00fang ta c\u00f3 2 c\u0103n c\u1ee7a a l\u00e0 \u221a a v\u00e0 -\u221a a . Tuy nhi\u00ean, trong \u0111\u00f3 ch\u1ec9 c\u00f3 \u221a a \u0111\u01b0\u1ee3c c\u00f4ng nh\u1eadn l\u00e0 c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc.<\/p>\n\n\n\n

V\u00ed d\u1ee5 minh h\u1ecda v\u1ec1 c\u0103n b\u1eadc 2 s\u1ed1 h\u1ecdc c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean b\u1ea5t k\u1ef3<\/p>\n\n\n\n

V\u00ed d\u1ee5, s\u1ed1 100 khai c\u0103n s\u1ebd c\u00f3 2 gi\u00e1 tr\u1ecb l\u00e0 \u221a 100 = 10 v\u00e0 -\u221a 100 = -10. Nh\u01b0ng th\u1ef1c ch\u1ea5t, trong \u0111\u00f3 ch\u1ec9 c\u00f3 \u221a 100 = 10 m\u1edbi \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc m\u00e0 th\u00f4i.<\/p>\n\n\n\n

Nh\u1eefng ch\u00fa \u00fd khi d\u00f9ng c\u00e1c ph\u00e9p to\u00e1n li\u00ean quan \u0111\u1ebfn c\u0103n b\u1eadc hai l\u1edbp 9<\/p>\n\n\n\n

To\u00e1n 9 c\u0103n b\u1eadc hai kh\u00f4ng ph\u1ea3i ph\u1ea7n ki\u1ebfn th\u1ee9c kh\u00f3 nh\u01b0ng khi \u00e1p d\u1ee5ng l\u1ea1i c\u00f3 kh\u00e1 nhi\u1ec1u ch\u00fa \u00fd c\u1ea7n c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> ph\u1ea3i l\u01b0u t\u00e2m. V\u00ec n\u1ebfu qu\u00ean m\u1ed9t trong c\u00e1c ch\u00fa \u00fd n\u00e0y, r\u1ea5t c\u00f3 th\u1ec3 s\u1ebd d\u1eabn \u0111\u1ebfn k\u1ebft qu\u1ea3 b\u00e0i l\u00e0m c\u1ee7a b\u1ea1n s\u1ebd b\u1ecb sai. Ch\u00fa \u00fd c\u1ee5 th\u1ec3 nh\u01b0 sau:<\/p>\n\n\n\n

V\u1edbi m\u1ed9t s\u1ed1 a \u2265 0, ta c\u00f3:<\/p>\n\n\n\n

N\u1ebfu x = \u221a a th\u00ec x \u2265 0 v\u00e0 x2= a.<\/p>\n\n\n\n

Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu x \u2265 0 v\u00e0 x2= a, th\u00ec x = \u221a a.<\/p>\n\n\n\n

C\u00e1ch vi\u1ebft ch\u00fa \u00fd theo k\u00ed hi\u1ec7u to\u00e1n h\u1ecdc<\/p>\n\n\n\n

\u0110\u1ecbnh l\u00ed v\u1ec1 so s\u00e1nh to\u00e1n 9 c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc<\/p>\n\n\n\n

\u0110\u1ec3 th\u1ef1c hi\u1ec7n ph\u00e9p so s\u00e1nh gi\u1eefa c\u00e1c c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc, ta s\u1eed d\u1ee5ng m\u1ed9t \u0111\u1ecbnh l\u00ed \u0111\u01a1n gi\u1ea3n l\u00e0: v\u1edbi m\u1ecdi s\u1ed1 a v\u00e0 b kh\u00f4ng \u00e2m (a,b \u2265 0) th\u00ec a < b \u21d4 \u221a a < \u221a b.<\/p>\n\n\n\n

V\u00ed d\u1ee5, do 9 <10 n\u00ean \u221a 9 < \u221a 10 \u21d4 3 < \u221a 10 .<\/p>\n\n\n\n

M\u1ed9t v\u00ed d\u1ee5 minh h\u1ecda kh\u00e1c khi \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd so s\u00e1nh c\u0103n b\u1eadc 2 s\u1ed1 h\u1ecdc<\/p>\n\n\n\n

Tr\u00ean \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 ki\u1ebfn th\u1ee9c m\u1edf \u0111\u1ea7u v\u1ec1 ph\u1ea7n c\u0103n b\u1eadc hai l\u1edbp 9 d\u00e0nh cho c\u00e1c b\u1ea1n h\u1ecdc sinh. V\u1edbi n\u1ec1n t\u1ea3ng n\u00e0y, c\u00e1c b\u1ea1n s\u1ebd v\u1eefng v\u00e0ng h\u01a1n khi \u0111\u01b0\u1ee3c b\u1ed5 sung th\u00eam nhi\u1ec1u ki\u1ebfn th\u1ee9c v\u1ec1 c\u0103n b\u1eadc hai \u1edf c\u00e1c b\u00e0i ti\u1ebfp theo. Ngo\u00e0i ra, \u0111\u1ec3 ph\u1ee5c v\u1ee5 cho nhu c\u1ea7u t\u00ecm hi\u1ec3u, h\u1ecdc t\u1eadp c\u1ee7a h\u1ecdc sinh t\u1eeb l\u1edbp 1 t\u1edbi l\u1edbp 12, Vietlearn cung c\u1ea5p t\u1ea5t c\u1ea3 n\u1ed9i dung b\u00e0i gi\u1ea3ng c\u0169ng nh\u01b0 tham kh\u1ea3o cho c\u00e1c b\u1ea1n t\u1ea1i Vietlearn.vn. H\u00e3y truy c\u1eadp ngay n\u00e0o!<\/p>\n\n\n\n

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

C\u0103n th\u1ee9c b\u1eadc hai v\u00e0 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c<\/p>\n\n\n\n

Li\u00ean h\u1ec7 gi\u1eefa ph\u00e9p nh\u00e2n v\u00e0 ph\u00e9p khai ph\u01b0\u01a1ng<\/p>\n\n\n\n

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

Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn Trong to\u00e1n h\u1ecdc, c\u0103n b\u1eadc 2 l\u00e0 ph\u1ea7n ki\u1ebfn th\u1ee9c tr\u1ecdng y\u1ebfu, b\u1ea1n b\u1eaft bu\u1ed9c ph\u1ea3i n\u1eafm \u0111\u01b0\u1ee3c nh\u1eefng ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n v\u1ec1 m\u1ea3ng n\u00e0y \u0111\u1ec3 tr\u00e1nh g\u1eb7p ph\u1ea3i nh\u1eefng sai s\u00f3t kh\u00f4ng \u0111\u00e1ng. Tuy nhi\u00ean, n\u1ebfu \u0111\u1ec3 h\u1ecdc m\u1ed9t l\u1ea7n h\u1ebft t\u1ea5t c\u1ea3 c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 […]<\/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-1109","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\/1109","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=1109"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1109\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=1109"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=1109"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=1109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}