Problem

Source:

Tags: InInquility, algebra



Let $a,b,c,d$ be positive real numbers such that $a+b+c+d=1$ prove that: ($\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+d}+\frac{d^2}{d+a})^5 \geq 5^5(\frac{ac}{27})^2$