CAT (QA) PYQs

$u² + (u − 2v − 1)² = −4v (u + v)$. Then the value of $u + 3v$ is

If $x + 1 = x^2$ and $x > 0$, then $2x^4$ is

If $x$ is a positive real number such that $x^8 + \frac{1}{x^8} = 47$, then the value of $x^9 + \frac{1}{x^9}$ is