अगर $x^{2}+y^{2}+z^{2}=2(x+z-1)$, तो इसका मूल्य: $x^{3}+y^{3}+z^ {3}=?$

$x^{2}+y^{2}+z^{2}=2(x+z-1)$

$\Rightarrow x^{2}+y^{2}+z^{2}=2 x+2 z-2$

$\Rightarrow x^{2}-2 x+y^{2}+z^{2}-2 z+2=0$

$\Rightarrow x^{2}-2 x+1+y^{2}+z^{2}-2 z+1=0$

$\Rightarrow(x-1)^{2}+y^{2}+(z-1)^{2}=0$

$\left[\because a^{2}+b^{2}+c^{2}=0 \Rightarrow a=0, b=0, c=0\right]$

$\therefore \quad x-1=0 \Rightarrow x=1$

$y=0$

$z-1=0 \Rightarrow z=1$

$\therefore \quad x^{3}+y^{3}+z^{3}=1+0+1=2$