General Help with inequalities... (1 Viewer)

[Js^-1]

Hey I don't really understand how to do the inequality questions. I get the basic ones, i.e. a<SUP>2</SUP>+b<SUP>2</SUP> > (ab)<SUP>1/2 </SUP>(Or equal to)
We kinda skipped over this in class and I can't find anything that explains how to do them.

Specifically, from the 2003 paper,

Prove (x)<SUP>1/2</SUP> + x > (x(x+1))<SUP>1/2 </SUP>(Or equal to)

 

[ronnknee]

Consider (x + root x)²
= x² + x + 2x.root x (note 2x.root x >= 0)
>= x² + x
= x(x + 1)

Therefore x + root x >= root [x(x + 1)]