Cho a,b,c > 0 sao cho a + b + c =1. Chứng minh

√b + √a + √c  ≥  33(ab + bc + ca)
thay vào r áp dụng cosi cho a^2 cộng √a/(3√3) cộng √a/(3√3) –  ๖ۣۜJinღ๖ۣۜKaido 19-04-17 08:47 AM
:) Gợi ý nhé $2(ab \dotplus bc \dotplus ca)=(1-a^2-b^2-c^2)$ –  .com 19-04-17 08:08 AM
thỏa mãn e ơi,thay số kĩ vào đi –  ๖ۣۜTQT☾♋☽ 18-04-17 09:21 AM
Phản chứng a=b=c=1/3 ko tm –  Mây 18-04-17 09:20 AM
Anh nói rõ cho em hiểu đề sai ở đâu vậy ? –  W2S 18-04-17 09:12 AM
Đề sai bn ơi –  Mây 18-04-17 08:32 AM
Anh giải hộ em đi ;c –  W2S 18-04-17 08:27 AM
chết,bấm nhầm –  ๖ۣۜTQT☾♋☽ 18-04-17 08:19 AM
thỏa mãn mà anh –  W2S 18-04-17 08:14 AM
sai đề r,cho x=y=z=1/3 k thỏa mãn –  ๖ۣۜTQT☾♋☽ 18-04-17 07:39 AM
Cách của Nam :)))
$ab+bc+ca=\frac{1-a^2-b^2-c^2}2$

Thay vào ta có BĐT

$\Leftrightarrow \sqrt a+\sqrt b+\sqrt c\ge3\sqrt3\frac{1-a^2-b^2-c^2}2$

$\Leftrightarrow 3\sqrt3(a^2+b^2+c^2)+2(\sqrt a+\sqrt b+\sqrt c)\ge3\sqrt3$

Sử dụng BĐT AM-GM ta có 

$3\sqrt3a^2+\sqrt a+\sqrt a\ge3\sqrt3a$

tương tự cộng lại ta có đpcm

Bạn cần đăng nhập để có thể gửi đáp án

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