Positive reals $a$ , $b$ and $c$ are such that $abc=1$ . Find the infimum value of

$\frac {a^3}{(a-b)(a-c)} + \frac {b^3}{(b-c)(b-a)} + \frac {c^3}{(c-a)(c-b)}$

Other problems: Check your Calibre

The answer is 3.000.

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Easy.It's easy to show that the sum equals $a+b+c$ using the given constraint $abc=1$ .Then use $AM-GM$ inequality to get $a+b+c>=3(abc)^(1/3)=3$ .So the Minimum is $3$