Prove that for all , such that , we have:

(Posed Here)

Prove that , for all such that , we have:

(Posted Here)[/hide]

For such that , prove that:

(Posted Here)

Prove that, for satisfying we always have:

(Posted Here; See post # 75)

For positive reals we have:

(Posted here)

For positive reals satisfying Find given :

(Posted here)

For positive reals prove that :

(I jumbled up other three inequalities of mine with this one; Posted here)

For Positive reals prove that:

(Posted Here)

For positive reals satisfying prove that:

(Posted Here)

Prove that , for satisfying :

(Posted here)

For Prove that:

(Posted here; Post #138)

Prove that for all positive reals we always have:

(Posted Here)

For , show that

(Posted here)

Given are the sides of a triangle, show that we have

(Not posted anywhere yet)

For all we have that

(Not posted anywhere yet;)

Note

Given such that , prove that we have

(Posted Here)

For all , show that

(Not posted Anywhere Yet)

(Sayan Mukherjee) For positive reals satisfying Prove that we have:

(Not posted Anywhere Yet)

Given positive reals ; Prove that we have

(Not posted Anywhere Yet)

(Proposed in the contest named War_inequality_Secondary at maths.vn as a part of Team 1)

For all , show that we have

Note

(Not posted Anywhere Yet)

Given , show that we have

(Posted here)

For positive reals show that we have

(Made while proving problem wrongly here)

Remark.

This is actually weaker than a problem by Tran Nguyen Quoc Cuong (mathstarofvn), which is on proving that

Which follows from the method in which I proved the previous inequality.

For positive reals , prove that we always have the following inequality:

(Not Posted Anywhere Yet)

(To be updated as soon as I make another new problem)