quoccuonglqd

Cho $a,b,c>0$ chứng minh

$\frac{3a}{\sqrt{2}(b+c)+(3-2\sqrt{2})\sqrt{bc}}+\frac{3b}{\sqrt{2}(c+a)+(3-2\sqrt{2})\sqrt{ca}}+\frac{3c}{\sqrt{2}(a+b)+(3-2\sqrt{2})\sqrt{ab}}\geqslant \sqrt{1+\frac{8(a^{2}+b^{2}+c^{2})}{ab+bc+ca}}$

 

Cho $a,b,c>0$,chứng minh

$a^{2}+b^{2}+c^{2}+\frac{2abc(a+b+c)}{ab+bc+ca}\geqslant \frac{5(ab+bc+ca)}{3}$

Cho $\frac{sin^{4}x}{a}+\frac{cos^{4}a}{b}=\frac{1}{a+b}$ với $a,b>0$

Chứng minh $\frac{sin^{8}x}{a^{3}}+\frac{cos^{8}x}{b^{3}}=\frac{1}{(a+b)^{3}}$