Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
C\u0103n b\u1eadc 3 la\u0300 m\u00f4\u0323t trong nh\u01b0\u0303ng ki\u00ea\u0301n th\u01b0\u0301c kh\u00f4ng th\u01b0\u0323c s\u1ef1 kho\u0301 n\u0103\u0301m b\u0103\u0301t. Tuy nhi\u00ean, nh\u01b0\u0303ng da\u0323ng toa\u0301n \u01b0\u0301ng du\u0323ng c\u0103n b\u1eadc 3 va\u0300o \u0111\u00ea\u0309 gia\u0309i quy\u00ea\u0301t la\u0323i kh\u00f4ng h\u00ea\u0300 \u0111\u01a1n gia\u0309n. Do \u0111o\u0301, ng\u01b0\u01a1\u0300i du\u0300ng c\u00e2\u0300n pha\u0309i n\u0103\u0301m ch\u0103\u0301c nh\u01b0\u0303ng ki\u00ea\u0301n th\u01b0\u0301c va\u0300 ti\u0301nh ch\u00e2\u0301t quan tro\u0323ng cu\u0309a c\u0103n b\u1eadc 3. T\u01b0\u0300 \u0111o\u0301 co\u0301 th\u00ea\u0309 v\u00e2\u0323n du\u0323ng m\u00f4\u0323t ca\u0301ch h\u01a1\u0323p ly\u0301 va\u0300o ca\u0301c ba\u0300i toa\u0301n. Ti\u00ea\u0301p tu\u0323c cu\u0300ng Vietlearn chinh phu\u0323c c\u0103n b\u1eadc 3 l\u1edbp 9 \u01a1\u0309 ngay ba\u0300i vi\u00ea\u0301t d\u01b0\u01a1\u0301i \u0111\u00e2y.<\/p>\n\n\n\n
\u00d4n t\u1eadp c\u0103n b\u1eadc 3 l\u1edbp 9<\/p>\n\n\n\n
C\u0103n b\u1eadc ba l\u00e0 g\u00ec?<\/p>\n\n\n\n
C\u0103n b\u1eadc ba cu\u0309a m\u00f4\u0323t s\u00f4\u0301 x b\u00e2\u0301t ky\u0300 la\u0300 a n\u00ea\u0301u nh\u01b0: a3 = x. C\u0103n b\u1eadc ba cu\u0309a x \u0111\u01b0\u01a1\u0323c ky\u0301 hi\u00ea\u0323u m\u00f4\u0323t ca\u0301ch \u0111\u01a1n gia\u0309n la\u0300 3\u221ax. Ky\u0301 hi\u00ea\u0323u na\u0300y gi\u00f4\u0301ng v\u01a1\u0301i c\u0103n b\u1eadc 2 nh\u01b0ng th\u00eam s\u00f4\u0301 3 \u01a1\u0309 ph\u00e2\u0300n \u0111\u00e2\u0300u cu\u0309a c\u0103n.<\/p>\n\n\n\n
Nh\u01b0\u0303ng s\u00f4\u0301 co\u0301 c\u0103n b\u1eadc 3 la\u0300 nh\u01b0\u0303ng s\u00f4\u0301 th\u01b0\u0323c. \u0110\u00e2y la\u0300 m\u00f4\u0323t trong nh\u01b0\u0303ng ti\u0301nh ch\u00e2\u0301t kha\u0301c v\u01a1\u0301i c\u0103n b\u1eadc 2 la\u0300 c\u0103n b\u1eadc ch\u0103\u0303n. c\u0103n b\u1eadc 2 y\u00eau c\u00e2\u0300u ca\u0301c s\u00f4\u0301 th\u01b0\u0323c kh\u00f4ng \u00e2m. c\u0103n b\u1eadc 3 thi\u0300 kh\u00f4ng pha\u0309i nh\u01b0 v\u00e2\u0323y. Vi\u0301 du\u0323: 3\u221a-8= -2<\/p>\n\n\n\n
Nh\u01b0\u0303ng ti\u0301nh ch\u00e2\u0301t c\u01a1 ba\u0309n cu\u0309a c\u0103n b\u1eadc 3 l\u1edbp 9<\/p>\n\n\n\n
Chu\u0301ng ta c\u00e2\u0300n quan t\u01a1\u0301i 3 ti\u0301nh ch\u00e2\u0301t c\u01a1 ba\u0309n nh\u00e2\u0301t cu\u0309a m\u00f4\u0323t c\u0103n b\u1eadc ba th\u00f4ng th\u01b0\u01a1\u0300ng. \u0110o\u0301 la\u0300:<\/p>\n\n\n\n
x < y \u2b04 3\u221ax < 3\u221ay<\/p>\n\n\n\n
3\u221ax.y = 3\u221ax . 3\u221ay<\/p>\n\n\n\n
Trong tr\u01b0\u01a1\u0300ng h\u01a1\u0323p y kha\u0301c 0 ta co\u0301:<\/p>\n\n\n\n
Ng\u01b0\u01a1\u0300i ta s\u01b0\u0309 du\u0323ng 3 ti\u0301nh ch\u00e2\u0301t c\u01a1 ba\u0309n tr\u00ean \u0111\u00e2y \u0111\u00ea\u0309 th\u01b0\u0323c hi\u00ea\u0323n ca\u0301c ba\u0300i toa\u0301n co\u0301 li\u00ean quan t\u01a1\u0301i c\u0103n b\u1eadc 3. Trong \u0111o\u0301, ti\u0301nh ch\u00e2\u0301t 2 va\u0300 3 la\u0300 nh\u01b0\u0303ng ti\u0301nh ch\u00e2\u0301t \u0111\u01b0\u01a1\u0323c s\u01b0\u0309 du\u0323ng nhi\u00ea\u0300u h\u01a1n ca\u0309.<\/p>\n\n\n\n
Ca\u0301c da\u0323ng ba\u0300i t\u00e2\u0323p ch\u01b0\u0301a c\u0103n b\u1eadc 3 l\u1edbp 9<\/p>\n\n\n\n
Cu\u0300ng \u0111i\u00ea\u0309m qua nh\u01b0\u0303ng da\u0323ng ba\u0300i t\u00e2\u0323p c\u01a1 ba\u0309n co\u0301 ch\u01b0\u0301a c\u0103n b\u1eadc 3 ho\u0103\u0323c c\u00e2\u0300n s\u01b0\u0309 du\u0323ng c\u0103n b\u1eadc 3 trong qua\u0301 tri\u0300nh la\u0300m ba\u0300i.<\/p>\n\n\n\n
C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp ch\u1ee9a c\u0103n b\u1eadc 3 l\u00e0 g\u00ec<\/p>\n\n\n\n
Da\u0323ng 1: Th\u01b0\u0323c hi\u00ea\u0323n phe\u0301p ti\u0301nh<\/p>\n\n\n\n
Th\u01b0\u0323c hi\u00ea\u0323n phe\u0301p ti\u0301nh la\u0300 da\u0323ng toa\u0301n c\u01a1 ba\u0309n nh\u00e2\u0301t cu\u0309a ca\u0301c ba\u0300i toa\u0301n li\u00ean quan t\u01a1\u0301i c\u0103n b\u1eadc hai c\u0103n b\u1eadc ba. \u0110\u00f4\u0301i v\u01a1\u0301i da\u0323ng ba\u0300i t\u00e2\u0323p na\u0300y thi\u0300 chu\u0309 y\u00ea\u0301u s\u01b0\u0309 du\u0323ng 2 c\u00f4ng th\u01b0\u0301c:<\/p>\n\n\n\n
3\u221ax3=x va\u0300 (3\u221ax)3 = x<\/p>\n\n\n\n
B\u00ean ca\u0323nh \u0111o\u0301, co\u0300n ph\u00f4\u0301i k\u00ea\u0301t h\u01a1\u0323p s\u01b0\u0309 du\u0323ng ca\u0301c h\u0103\u0300ng \u0111\u0103\u0309ng th\u01b0\u0301c l\u00e2\u0323p ph\u01b0\u01a1ng nh\u01b0: l\u00e2\u0323p ph\u01b0\u01a1ng cu\u0309a m\u00f4\u0323t t\u00f4\u0309ng, l\u00e2\u0323p ph\u01b0\u01a1ng cu\u0309a m\u00f4\u0323t hi\u00ea\u0323u, t\u00f4\u0309ng 2 l\u00e2\u0323p ph\u01b0\u01a1ng, hi\u00ea\u0323u 2 l\u00e2\u0323p ph\u01b0\u01a1ng.<\/p>\n\n\n\n
Da\u0323ng 2: Ch\u01b0\u0301ng minh \u0111\u0103\u0309ng th\u01b0\u0301c, b\u00e2\u0301t \u0111\u0103\u0309ng th\u01b0\u0301c<\/p>\n\n\n\n
\u0110\u00e2y cu\u0303ng la\u0300 m\u00f4\u0323t trong nh\u01b0\u0303ng da\u0323ng toa\u0301n kha\u0301 ph\u00f4\u0309 bi\u00ea\u0301n co\u0301 s\u01b0\u0309 du\u0323ng gi\u1ea3i toa\u0301n 9 c\u0103n b\u1eadc ba. Kh\u00f4ng co\u0301 ph\u01b0\u01a1ng pha\u0301p gia\u0309i chung cho da\u0323ng toa\u0301n na\u0300y. Th\u00f4ng th\u01b0\u01a1\u0300ng, co\u0301 th\u00ea\u0309 la\u0300 ti\u0301nh toa\u0301n tr\u01b0\u0323c ti\u00ea\u0301p, ru\u0301t go\u0323n,\u2026 \u0110\u00f4\u0301i v\u01a1\u0301i ca\u0301c ba\u0300i toa\u0301n ph\u01b0\u0301c ta\u0323p thi\u0300 th\u01b0\u01a1\u0300ng la\u0300 ru\u0301t go\u0323n v\u00ea\u0300 da\u0323ng \u0111\u01a1n gia\u0309n h\u01a1n \u0111\u00ea\u0309 ch\u01b0\u0301ng minh. S\u01b0\u0309 du\u0323ng ph\u00f4\u0301i k\u00ea\u0301t h\u01a1\u0323p 3 ti\u0301nh ch\u00e2\u0301t phi\u0301a tr\u00ean \u0111\u00ea\u0309 la\u0300m ba\u0300i.<\/p>\n\n\n\n
Da\u0323ng 3: So sa\u0301nh hai c\u0103n b\u1eadc 3<\/p>\n\n\n\n
So sa\u0301nh hai c\u0103n b\u1eadc 3 la\u0300 da\u0323ng toa\u0301n c\u01a1 ba\u0309n co\u0300n la\u0323i cu\u0309a ca\u0301c ba\u0300i toa\u0301n li\u00ean quan t\u01a1\u0301i c\u0103n b\u1eadc 3. \u0110\u00e2y kh\u00f4ng pha\u0309i da\u0323ng toa\u0301n kho\u0301 n\u00ea\u0301u chi\u0309 so sa\u0301nh hai c\u0103n b\u1eadc 3 th\u00f4ng th\u01b0\u01a1\u0300ng. V\u00e2\u0303n s\u01b0\u0309 du\u0323ng ph\u01b0\u01a1ng pha\u0301p X < Y \u2b04 3\u221aX< 3\u221aY<\/p>\n\n\n\n
\u0110\u00f4\u0301i v\u01a1\u0301i ca\u0301c ba\u0300i toa\u0301n c\u0103n b\u1eadc ba l\u1edbp 9 n\u00e2ng cao thi\u0300 c\u00e2\u0300n \u0111\u01b0a v\u00ea\u0300 da\u0323ng \u0111\u01a1n gia\u0309n b\u0103\u0300ng ca\u0301ch ph\u00e2n ti\u0301ch nh\u00e2n t\u01b0\u0309, h\u0103\u0300ng \u0111\u0103\u0309ng th\u01b0\u0301c,\u2026 \u0111\u00ea\u0309 co\u0301 th\u00ea\u0309 gia\u0309i quy\u00ea\u0301t<\/p>\n\n\n\n
Tr\u0103\u0301c nghi\u00ea\u0323m c\u0103n b\u1eadc 3 l\u1edbp 9<\/p>\n\n\n\n
Vietlearn co\u0301 m\u00f4\u0323t s\u00f4\u0301 ba\u0300i t\u00e2\u0323p tr\u0103\u0301c nghi\u00ea\u0323m li\u00ean quan t\u01a1\u0301i gia\u0309i toa\u0301n 9 c\u0103n b\u1eadc 3 mu\u00f4\u0301n cung c\u00e2\u0301p cho ba\u0323n \u0111o\u0323c. \u0110\u00e2y la\u0300 ca\u0301c ba\u0300i t\u00e2\u0323p t\u01b0\u01a1ng \u0111\u00f4\u0301i \u0111\u01a1n gia\u0309n da\u0300nh cho nh\u01b0\u0303ng ng\u01b0\u01a1\u0300i m\u01a1\u0301i la\u0300m quen v\u01a1\u0301i da\u0323ng toa\u0301n c\u0103n b\u1eadc ba l\u1edbp 9.<\/p>\n\n\n\n
Gi\u1ea3i m\u00e3 tr\u1eafc nghi\u1ec7m c\u0103n b\u1eadc 3 l\u1edbp 9<\/p>\n\n\n\n
C\u00e2u 1: c\u0103n b\u1eadc 3 cu\u0309a 9 ki\u0301 hi\u00ea\u0323u la\u0300 gi\u0300?<\/p>\n\n\n\n
3\u221a9<\/p>\n\n\n\n
9<\/p>\n\n\n\n
9\u221a3<\/p>\n\n\n\n
2\u221a9<\/p>\n\n\n\n
D\u01b0\u0323a va\u0300o kha\u0301i ni\u00ea\u0323m cu\u0309a c\u0103n b\u1eadc 3. c\u0103n b\u1eadc 3 cu\u0309a 9 se\u0303 \u0111\u01b0\u01a1\u0323c vi\u00ea\u0301t d\u01b0\u01a1\u0301i da\u0323ng 3\u221a9.<\/p>\n\n\n\n
Cho\u0323n A.<\/p>\n\n\n\n
C\u00e2u 2: K\u00ea\u0301t qua\u0309 cu\u0309a phe\u0301p ti\u0301nh 3\u221a27 \u2013 3\u221a125 la\u0300 gi\u0300?<\/p>\n\n\n\n
2<\/p>\n\n\n\n
-2<\/p>\n\n\n\n
3\u221a98<\/p>\n\n\n\n
\u20133\u221a98<\/p>\n\n\n\n
Ta co\u0301: 3\u221a27 \u2013 3\u221a125 = 3 \u2013 5 = -2.<\/p>\n\n\n\n
Cho\u0323n B.<\/p>\n\n\n\n
C\u00e2u 3: Ti\u0300m gia\u0301 tri\u0323 cu\u0309a x \u0111\u00ea\u0309 co\u0301 nghi\u0303a. Cho\u0323n c\u00e2u \u0111u\u0301ng nh\u00e2\u0301t.<\/p>\n\n\n\n
x = 4<\/p>\n\n\n\n
x = 5<\/p>\n\n\n\n
x= 8<\/p>\n\n\n\n
x la\u0300 s\u00f4\u0301 th\u01b0\u0323c<\/p>\n\n\n\n
T\u00e2\u0301t ca\u0309 ca\u0301c s\u00f4\u0301 th\u01b0\u0323c \u0111\u00ea\u0300u co\u0301 c\u0103n b\u1eadc 3. Do \u0111o\u0301 \u0111\u00ea\u0309 co\u0301 nghi\u0303a thi\u0300 16x -5 pha\u0309i la\u0300 s\u00f4\u0301 th\u01b0\u0323c => x la\u0300 s\u00f4\u0301 th\u01b0\u0323c.<\/p>\n\n\n\n
Cho\u0323n D.<\/p>\n\n\n\n
C\u00e2u 4: K\u1ebft qu\u1ea3 c\u1ee7a ph\u00e9p t\u00ednh l\u00e0 g\u00ec?<\/p>\n\n\n\n
14<\/p>\n\n\n\n
16<\/p>\n\n\n\n
18<\/p>\n\n\n\n
12<\/p>\n\n\n\n
Ta c\u00f3: =2-(-6)+8=16<\/p>\n\n\n\n
Ch\u1ecdn B.<\/p>\n\n\n\n
C\u00e2u 5: R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c:<\/p>\n\n\n\n
a + b<\/p>\n\n\n\n
a \u2013 b<\/p>\n\n\n\n
a.b<\/p>\n\n\n\n
a\/b<\/p>\n\n\n\n
S\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c hi\u1ec7u 2 l\u1eadp ph\u01b0\u01a1ng ta \u0111\u01b0\u1ee3c:=(3\u221aa)3 \u2013 (3\u221ab)3 = a \u2013 b.<\/p>\n\n\n\n
Ch\u1ecdn B.<\/p>\n\n\n\n
C\u00e2u 6: Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh (23\u221ax+5)(23\u221ax-5)=-21<\/p>\n\n\n\n
x = -1<\/p>\n\n\n\n
x = 3<\/p>\n\n\n\n
x = -1 ho\u1eb7c x = 1<\/p>\n\n\n\n
x = 3 ho\u1eb7c x = -3<\/p>\n\n\n\n
S\u1eed d\u1ee5ng h\u1eb1ng \u0111\u1eb3ng th\u1ee9c ta \u0111\u01b0\u1ee3c: (23\u221ax)2 \u2013 25 = -21=> 43\u221ax2=4=> x2=1. V\u1eady x = 1 ho\u1eb7c x = -1.<\/p>\n\n\n\n
Ch\u1ecdn C.<\/p>\n\n\n\n
C\u00e2u 7: \u0110\u00e2u kh\u00f4ng ph\u1ea3i l\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a c\u0103n b\u1eadc ba.<\/p>\n\n\n\n
x < y \u2b04 3\u221ax < 3\u221ay<\/p>\n\n\n\n
3\u221ax.y = 3\u221ax . 3\u221ay<\/p>\n\n\n\n
x = y \u2b04 3\u221ax < y<\/p>\n\n\n\n
D\u1ef1a v\u00e0o c\u00e1c t\u00ednh ch\u1ea5t li\u1ec7t k\u00ea \u1edf ph\u1ea7n \u0111\u1ea7u, d\u1ec5 nh\u1eadn th\u1ea5y c\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a c\u0103n b\u1eadc ba bao g\u1ed3m c\u00e1c \u0111\u00e1p \u00e1n A, B v\u00e0 C.<\/p>\n\n\n\n
Ch\u1ecdn D.<\/p>\n\n\n\n
Tr\u00ean \u0111\u00e2y l\u00e0 to\u00e0n b\u1ed9 nh\u1eefng ki\u1ebfn th\u1ee9c v\u1ec1 c\u0103n b\u1eadc 3 l\u1edbp 9 d\u00e0nh cho b\u1ea1n \u0111\u1ecdc tham kh\u1ea3o. \u0110\u1ec3 c\u00f3 th\u1ec3 h\u1ecdc t\u1ed1t to\u00e1n 9 th\u00ec c\u0103n b\u1eadc 3 ch\u1eafc ch\u1eafn l\u00e0 ki\u1ebfn th\u1ee9c kh\u00f4ng th\u1ec3 b\u1ecf qua. C\u00f2n ch\u1ea7n ch\u1edd g\u00ec n\u1eefa khi kh\u00f4ng \u0111\u1ed3ng h\u00e0nh c\u00f9ng Vietlearn \u0111i chinh ph\u1ee5c c\u00e1c d\u1ea1ng to\u00e1n m\u1edbi l\u1ea1 nh\u1ea5t.<\/p>\n\n\n\n
<\/p>\n\n\n\n
R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c l\u1edbp 9<\/p>\n\n\n\n
C\u0103n b\u1eadc hai l\u1edbp 9 \u2013 Kh\u00e1i ni\u1ec7m v\u00e0 c\u00e1c \u0111\u1ecbnh l\u00fd li\u00ean quan<\/p>\n\n\n\n
Bi\u1ebfn<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn C\u0103n b\u1eadc 3 la\u0300 m\u00f4\u0323t trong nh\u01b0\u0303ng ki\u00ea\u0301n th\u01b0\u0301c kh\u00f4ng th\u01b0\u0323c s\u1ef1 kho\u0301 n\u0103\u0301m b\u0103\u0301t. Tuy nhi\u00ean, nh\u01b0\u0303ng da\u0323ng toa\u0301n \u01b0\u0301ng du\u0323ng c\u0103n b\u1eadc 3 va\u0300o \u0111\u00ea\u0309 gia\u0309i quy\u00ea\u0301t la\u0323i kh\u00f4ng h\u00ea\u0300 \u0111\u01a1n gia\u0309n. Do \u0111o\u0301, ng\u01b0\u01a1\u0300i du\u0300ng c\u00e2\u0300n pha\u0309i n\u0103\u0301m ch\u0103\u0301c nh\u01b0\u0303ng ki\u00ea\u0301n th\u01b0\u0301c va\u0300 ti\u0301nh ch\u00e2\u0301t quan […]<\/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-1089","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\/1089","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=1089"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1089\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=1089"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=1089"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=1089"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}