Hello..
I need help to prove this inequalities
I don't know how good you are at inequalities but it basically goes like this:
$\displaystyle \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} = $ $\displaystyle \frac{a^2cd}{abcd} + \frac{b^2ad}{abcd} + \frac{c^2ab}{abcd} + \frac{d^2bc}{abcd}$
$\displaystyle = \frac{a^2cd + b^2ad + c^2ab + d^2bc}{abcd} \leq \frac{a^2 + b^2 + c^2 + d^2}{abcd}$ $\displaystyle \leq \frac{a + b + c + d}{abcd} \leq \frac{4}{abcd}$
So, $\displaystyle \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a} \leq \frac{4}{abcd}$