Question 51
Let $x$ and $y$ be positive real numbers with $x + y = 1$.
Prove that
$$
\frac{(3x - 1)^2}{x} + \frac{(3y - 1)^2}{y} \geq 1.
$$
When does equality hold?
Prove that
$$
\frac{(3x - 1)^2}{x} + \frac{(3y - 1)^2}{y} \geq 1.
$$
When does equality hold?