My question is about the following inequality:
If abc=1 and a,b,c different than 1, then prove
$\displaystyle \displaystyle \frac{a^{2}}{{(a-1)^{2}}}+\frac{b^{2}}{{(b-1)^{2}}}+\frac{c^{2}}{{(c-1)^{2}}}\ge 1 $
My question is about the following inequality:
If abc=1 and a,b,c different than 1, then prove
$\displaystyle \displaystyle \frac{a^{2}}{{(a-1)^{2}}}+\frac{b^{2}}{{(b-1)^{2}}}+\frac{c^{2}}{{(c-1)^{2}}}\ge 1 $