Tenth Philippine Mathematical Olympiad

Solution:
$x^{4}-10x^{2}+1$

We let $x=\sqrt{3}-\sqrt{2}$. We find the monic polynomial equation of least degree in terms of $x$. Squaring, we get
$$x^{2}=(\sqrt{3}-\sqrt{2})^{2}=5-2\sqrt{6} \quad \text{or} \quad x^{2}-5=-2\sqrt{6}$$
Squaring the last equation, we finally get
$$\left(x^{2}-5\right)^{2}=(-2\sqrt{6})^{2} \quad \text{or} \quad x^{4}-10x^{2}+1=0$$