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Inequality

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/0:
Prove for WITHOUT CALCULUS

kamil9876:
You can use the method i used for Ahmad's problem:
http://vcenotes.com/forum/index.php/topic,2398.msg140527.html#msg140527

checkout the problem in my second post of that thread, it has a similair strategy too :)

Your problem:

It's true for x=1. if increase x from 1 to 1+a:

then the expression: becomes:


(1)


obviously -1<a since x is positive. If a was positive then [/tex] and so
is positive which means that expression 1 is greater than two as required. However if -1<a<0 then let a=-b and so 0<b<1.



But obviously has a larger modulus than b. and so    is positive in this case too.

/0:
nice! thanks kamil

Mao:






, which is true

TrueTears:
Interesting methods lol

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