1. For what values of $x, y, z$ does the expression $x^{2}+y^{2}+z^{2}-12 y-14 z+90$ have the minimum value? Determine that value.
Solution. We obtain sequentially

$$
\begin{aligned}
x^{2}+y^{2}+z^{2}-12 y-14 z+90 & =x^{2}+y^{2}-12 y+z^{2}-14 z+90 \\
& =x^{2}+(y-6)^{2}+(z-7)^{2}+5 \geq 5
\end{aligned}
$$

According to this, the smallest possible value of the given expression is 5, and it is achieved for $x=0, y=6, z=7$.