Form the equation of the lowest degree with rational coefficients which has $2+\sqrt{3}$ and $3+\sqrt{2}$ as two of its roots
I tried taking $x=2+\sqrt{3}$, $3+\sqrt{2}$ and also $y=\sqrt{3}$, $y=\sqrt{2}$ but got no results. The equation becomes too complicated and the degree of $x$ becomes too much (greater than $4$).
The answer is $x^4-10^3+32x^2-34x+7$