Challenge problem:
Given:
1) with
2) ,where are the roots of the above equation
Prove:
Moderator approved, CB
Here is what I did.
By Vieta's formulas, we have , and . Then . And then, .
Now, we have , and since we arrive at (*) .
Eventually, . Notice that because .
It follows that ( is positive).
Also from (*), and it follows that .
From all this we get the inequality: .