2
$\begingroup$

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.

  • 1
    If this is homework, then what have you tried before?2012-03-07

2 Answers 2