Cho $a,b,c >0$
Chứng minh $\sqrt{\frac{a^3}{a^3+(b+c)^3}} + \sqrt{\frac{b^3}{b^3+(a+c)^3}} + \sqrt{\frac{c^3}{c^3+(b+a)^3}} \geq 1$
Cho $a,b,c >0$
Chứng minh $\sqrt{\frac{a^3}{a^3+(b+c)^3}} + \sqrt{\frac{b^3}{b^3+(a+c)^3}} + \sqrt{\frac{c^3}{c^3+(b+a)^3}} \geq 1$
Cho $a,b,c >0$
Chứng minh $\sqrt{\frac{a^3}{a^3+(b+c)^3}} + \sqrt{\frac{b^3}{b^3+(a+c)^3}} + \sqrt{\frac{c^3}{c^3+(b+a)^3}} \geq 1$
$\sum\sqrt{\frac{a^{3}}{a^{3}+(b+c)^{3}}}\doteq \sum \sqrt{\frac{a^{3}}{(a+b+c)((b+c)^{2}-a(b+c)+a^{2})}}\geq \sum\frac{a^{2}}{\sqrt{a(a+b+c)(2(b^{2}+c^{2})-ab-ac+a^{2})}}\geq \sum\frac{a^{2}}{\frac{a^{2}+ab+bc+2(b^{2}+c^{2})-ab-ac+a^{2}}{2}}= \sum \frac{a^{2}}{a^{2}+b^{2}+c^{2}}=1$
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