18. Let $x$ and $y$ be real numbers satisfying the inequality
$$
5 x^{2}+y^{2}-4 x y+24 \leq 10 x-1 \text {. }
$$

Find the value of $x^{2}+y^{2}$.
18. Answer: 125
The inequality is equivalent to
$$
(x-5)^{2}+(2 x-y)^{2} \leq 0 .
$$

Thus we must have $(x-5)=0$ and $(2 x-y)=0$, hence $x^{2}+y^{2}=5^{2}+10^{2}=125$.