For what values of $a$ and $b$ does the expression $p=2 a^{2}-8 a b+17 b^{2}-16 a-4 b+2044$ take its minimum value? What is this value?
$p=2(a-2 b-4)^{2}+9(b-2)^{2}+1976 \geq 1976$. The equality $p=1976$ is possible if $b=2, a-2 b-4=0$, that is, when $a=8, b=2$.

## Answer

When $a=8, b=2 ; 1976$.