Let $a,b$ and $c$ three positive reals numbers such that $abc=1$. Define the function $f$ by $f(x)=\frac{^1}{1+(n-1)x^n}$ where $n$ is a positive integer. Prove that
$$a^2f\left(\frac{b}{a}\right)+b^2f\left(\frac{c}{b}\right)+c^2f\left(\frac{a}{c}\right)\ge\frac{3}{n}$$
I tried Jensen's inequality but got nothing.
Thanks for any help.