1. Given $x=\frac{5}{\sqrt{7}+\sqrt{2}}$. Then $\sqrt{2}$ can be expressed as a rational-coefficient cubic polynomial in terms of $x$ as $\qquad$ .
2. $-\frac{1}{10} x^{3}+\frac{13}{10} x$.
Notice that
$$
x=\frac{5}{\sqrt{7}+\sqrt{2}}=\sqrt{7}-\sqrt{2} \Rightarrow x+\sqrt{2}=\sqrt{7} \text {. }
$$

Square both sides and simplify to get $x^{2}=5-2 \sqrt{2} x$.
Multiply both sides of the above equation by $x$ to get
$$
\begin{array}{l}
x^{3}=5 x-2 \sqrt{2} x^{2}=5 x-2 \sqrt{2}(5-2 \sqrt{2} x) \\
\Rightarrow 10 \sqrt{2}=-x^{3}+13 x \\
\Rightarrow \sqrt{2}=-\frac{1}{10} x^{3}+\frac{13}{10} x .
\end{array}
$$