Đề : \(x\ge0\). Cm: \(\frac{2x}{3}+\frac{9}{\left(x+3\right)^2}\ge1\)
+ Theo BĐT Cauchy :
\(\frac{2x}{3}+\frac{9}{\left(x+3\right)^2}=\frac{x+3}{3}+\frac{x+3}{3}+\frac{9}{\left(x+3\right)^2}-2\)
\(\ge3\sqrt[3]{\frac{x+3}{3}\cdot\frac{x+3}{3}\cdot\frac{9}{\left(x+3\right)^2}}-2=3-2=1\)
Dấu "=" \(\Leftrightarrow\frac{x+3}{3}=\frac{9}{\left(x+3\right)^2}\Leftrightarrow x=0\)