IIM Kozhikode (QA) PYQs

If $x = \sqrt[3]{28}$ and $y = \sqrt[3]{27}$, find the value of $x + y - \frac{1}{x^2+xy+y^2}$.

Say $y = 3\sqrt{2} - 4$, find $y^2 + \frac{1}{y^2}$.