Ta có \(A=9x^2+9y^2+25z^2\)
\(=5\left(x^2+y^2\right)+\left(4x^2+25z^2\right)+\left(4y^2+25z^2\right)\)
\(\ge5.2\sqrt{x^2y^2}+2\sqrt{4x^2.25z^2}+2\sqrt{4y^2.25z^2}\)
\(=10xy+20xz+20yz\)
\(=10\left(xy+2xz+2yz\right)=10.65=650\)
Đẳng thức xảy ra \(\Leftrightarrow\) \(\hept{\begin{cases}x=y\\4x^2=25z^2\\4y^2=25z^2\end{cases}}\) và \(xy+2xz+2yz=65\)
\(\Leftrightarrow\) \(\hept{\begin{cases}x=y=5\\z=2\end{cases}}\)