Câu hỏi 23
Cho các số thực dương $a,b,c$ thỏa mãn $abc=1$. Chứng minh
$$\begin{aligned}&\frac1{\sqrt{a^3+2b^3+6}}+\frac1{\sqrt{b^3+2c^3+6}}+\frac1{\sqrt{c^3+2a^3+6}}\\&\le\frac{a^2}{\sqrt{a^4+4b+4c}}+\frac{b^2}{\sqrt{b^4+4c+4a}}+\frac{c^2}{\sqrt{c^4+4a+4b}}.\end{aligned}$$
$$\begin{aligned}&\frac1{\sqrt{a^3+2b^3+6}}+\frac1{\sqrt{b^3+2c^3+6}}+\frac1{\sqrt{c^3+2a^3+6}}\\&\le\frac{a^2}{\sqrt{a^4+4b+4c}}+\frac{b^2}{\sqrt{b^4+4c+4a}}+\frac{c^2}{\sqrt{c^4+4a+4b}}.\end{aligned}$$