x căn (1-y^2)+y căn (1-z^2)+ z căn (1-x^2)=3/2 tính x^2+y^2+z^2

$\begin{array}{l}
x\sqrt {1 - {y^2}}  + y\sqrt {1 - {z^2}}  + z\sqrt {1 - {x^2}}  = \dfrac{3}{2}\\
 \Leftrightarrow 2x\sqrt {1 - {y^2}}  + 2y\sqrt {1 - {z^2}}  + 2z\sqrt {1 - {x^2}}  = 3\\
 \Leftrightarrow 3 - 2x\sqrt {1 - {y^2}}  + 2y\sqrt {1 - {z^2}}  + 2z\sqrt {1 - {x^2}}  = 0\\
 \Leftrightarrow \left( {{x^2} - 2x\sqrt {1 - {y^2}}  + 1 - {y^2}} \right) + \left( {{y^2} - 2y\sqrt {1 - {z^2}}  + 1 - {z^2}} \right)\\
 + \left( {{z^2} - 2z\sqrt {1 - {x^2}}  + 1 - {x^2}} \right) = 0\\
 \Leftrightarrow {\left( {x - \sqrt {1 - {y^2}} } \right)^2} + {\left( {y - \sqrt {1 - {z^2}} } \right)^2} + {\left( {z - \sqrt {1 - {x^2}} } \right)^2} = 0\\
 \Leftrightarrow \left\{ \begin{array}{l}
x = \sqrt {1 - {y^2}} \\
y = \sqrt {1 - {z^2}} \\
z = \sqrt {1 - {x^2}} 
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
{x^2} = 1 - {y^2}\\
{y^2} = 1 - {z^2}\\
{z^2} = 1 - {x^2}
\end{array} \right.\\
 \Rightarrow 2\left( {{x^2} + {y^2} + {z^2}} \right) = 3\\
 \Rightarrow {x^2} + {y^2} + {z^2} = \dfrac{3}{2}
\end{array}$