If p , q , r are all positive numbers.
And if
p + q + r =1
then what is the least value of
$\left(\frac{1-p}{p}\right) \left(\frac{1-q}{q}\right) \left(\frac{1-r}{r}\right) $ ?
I begin with keeping 1-p = q + r
So the expression becomes
$\left(\frac{q+r}{p}\right) \left(\frac{p+r}{q}\right) \left(\frac{p+q}{r}\right) $
And then i try to use A.M. >= G.M inequality. But cant get to the answer.
Thanks in advance.