Let $a, b, c, d$ be positive real numbers, such that $a+b+c+d=4 $ prove : $\frac{4}{abcd} \geq \frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}$
Prove the inequality $a^2bc+b^2cd+c^2da+d^2ab \leq 4$ with $a+b+c+d=4$