Question 117
Let a, b, c, d be positive real numbers satisfying $a + b + c + d = 4$. Prove that:
$$
\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{d} + \frac{d^2}{a} \geq 4 + (a-d)^2.
$$
$$
\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{d} + \frac{d^2}{a} \geq 4 + (a-d)^2.
$$