Finding all solutions of the equation $(x^2 + y^2 + z^2 − 1)^2 + (x + y + z − 3)^2 = 0$. Find all solutions of the equation
$(x^2 + y^2 + z^2 − 1)^2 + (x + y + z − 3)^2 = 0$.    

not getting any clue.can somebody help me please.thanks.

I assume we are looking for real solutions. Then our equation is equivalent to the system $x^2+y^2+z^2=1$, $x+y+z=3$. 
Note that because $x^2+y^2+z^2=1$, the absolute values of $x$, $y$, and $z$ are $\le 1$, and they are not all $1$. 
Thus $|x+y+z|\le |x|+|y|+|z| \lt 3$. 
