Question 50
A number is rational if it can be written as $p/q$ with integers $p,q$. A real number that is not rational is called irrational. For example, $1/4$ is rational and $\sqrt3$ is irrational. Find all pairs of rational numbers $(a,b)$ such that
$$
\sqrt{a}+\sqrt{b}=\sqrt{2+\sqrt{3}}
$$
$$
\sqrt{a}+\sqrt{b}=\sqrt{2+\sqrt{3}}
$$