- Prove that if and , then
- Similarly to the previous problem:
Prove that if and , then
- Let's generalize the problems above:
Prove that if , , , and then
.Find the maximum possible value of .
I post the remaining separately because a small trick there, wont work any longer
I will directly attack the generalization,
Denote LHS of your inequality by I,
But by (*),
Equality for all s equal.
K cant get any better than that because we showed equality achieving