*Problem:*

If are the positive real roots of the equation prove that

.

*Solution:*

Let us divide both sides by and then cube them.

We acquire

.

But from Viete’s relations we have that

and .

So our inequality transforms into

,

or

.

So, it suffices to prove that

.

But the last inequality holds because

.

Adding up the cyclic relations we come to the desired inequality, *Q.E.D.*

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