RMO inequality problem If $a,b,c,d,e>1$, then prove that:
$$\frac{a^2}{b-1} + \frac{b^2}{c-1} + \frac{d^2}{e-1} + \frac{c^2}{a-1} + \frac{e^2}{d-1} \ge 20. $$
I don't know how to begin. What should be the approach?

By Cauchy Schwarz, $($given expression$)(a+b+c+d+e-5)\geq(a+b+c+d+e)^2$
Now this shows $($given expression$)\geq \dfrac{(a+b+c+d+e)^2}{a+b+c+d+e-5}$
Now $(a+b+c+d+e)^2=(a+b+c+d+e-5)^2+2\times(a+b+c+d+e-5)\times 5+25$ hence on division by $a+b+c+d+e-5$ we get $a+b+c+d+e-5+10+\dfrac{25}{a+b+c+d+e-5}=(a+b+c+d+e-5)+\dfrac{25}{a+b+c+d+e-5}+10$
Letting $x=a+b+c+d+e-5$ we note $x\geq0$ and the above is $x+\dfrac{25}{x}+10\geq 10+10=20$ by AM-GM.
