\(\frac{x^2}{2}+\frac{y^2}{3}+\frac{z^2}{4}=\frac{x^2}{5}+\frac{y^2}{5}+\frac{z^2}{5}\)
\(\Rightarrow\frac{x^2}{2}+\frac{y^2}{3}+\frac{z^2}{4}-\frac{x^2}{5}-\frac{y^2}{5}-\frac{z^2}{5}=0\)
\(\Rightarrow\left(\frac{x^2}{2}-\frac{x^2}{5}\right)+\left(\frac{y^2}{3}-\frac{y^2}{5}\right)+\left(\frac{z^2}{4}-\frac{z^2}{5}\right)=0\)
\(\Rightarrow x^2\left(\frac{1}{2}-\frac{1}{5}\right)+y^2\left(\frac{1}{3}-\frac{1}{5}\right)+z^2\left(\frac{1}{4}-\frac{1}{5}\right)=0\)
Mà \(x^2\left(\frac{1}{2}-\frac{1}{5}\right)+y^2\left(\frac{1}{3}-\frac{1}{5}\right)+z^2\left(\frac{1}{4}-\frac{1}{5}\right)\ge0\)
Xảy ra khi \(\hept{\begin{cases}x^2\left(\frac{1}{2}-\frac{1}{5}\right)=0\\y^2\left(\frac{1}{3}-\frac{1}{5}\right)=0\\z^2\left(\frac{1}{4}-\frac{1}{5}\right)=0\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x^2=0\\y^2=0\\z^2=0\end{cases}}\)\(\Rightarrow x=y=z=0\)
