10.4. Find a polynomial with integer coefficients for which the number $\sqrt{2}+\sqrt{3}$ is a root.
10.4. Let $x=\sqrt{2}+\sqrt{3}$. Then $x^{2}=5+2 \sqrt{6}$ and $\left(x^{2}-5\right)^{2}=24$, i.e., $x^{4}-10 x^{2}+1=0$.