If a and b are rational and b is not perfect square, then the...

We know that, in a quadratic equation with rational co-efficient, surd roots occur in conjugate pairs. So, other root will be $3 a-\sqrt{b}$. Quadratic equation will be $x^2-($ sum of roots $) x+$ Product of roots $=0$$\begin{aligned} x^2-(3 a-\sqrt{b}+3 a-\sqrt{b}) x +(3 a+\sqrt{b})(3 a-\sqrt{b})=0 \end{aligned}$$$or,$x^2-6 a x+9 a^2-b=0$