Find a monic polynomial of degree $4,$ in $x,$ with rational coefficients such that $\sqrt{2} +\sqrt{3}$ is a root of the polynomial.
Question:
Find a monic polynomial of degree $4,$ in $x,$ with rational coefficients such that $\sqrt{2} +\sqrt{3}$ is a root of the polynomial.
Answer:
Let's think step by step.

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x^4-10x^2+1
Find a monic polynomial of degree $4,$ in $x,$ with rational coefficients such that $\sqrt{2} +\sqrt{3}$ is a root of the polynomial.
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