Prove that if x, y, and z are positive real numbers, then
I haven't done much with inequalities so please explain your steps, thanks!
This is Nesbitts inequality, I know many proofs for this. Nesbitt's inequality - Wikipedia, the free encyclopedia
The above link proves it using AM-GM and Rearrangement inequality
I know a few more too
I will post them if you want
Define
THus: ; ;
So we have to prove:
Let: which is clearly convex in (use the second derivative)
It follows from Jensen's Inequality that:
Therefore:
Now remember that: and the assertion follows
Jensen's inequality - Wikipedia, the free encyclopedia