IIT JEE , AIEEE Forum - Mathematics , Algebra

Discussion Response Post to: For your recreation

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25 Mar 2008 14:46:56 IST

Subject: Re:For your recreation

hsbhatt (4440)

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If you let $a = 2^x ext {and} b = 3^x$

Then we are asked to prove that a+b+ab leq a^2+b^2+1

This is true as $1+a^2 geq 2a, 1+b^2 geq 2b ext{and} a^2+b^2 geq 2ab$

Ok that is a strict inequality

PS: I could have just said use the inequality

$p^2 + q^2 + r^2 \geq pq+qr+rp$

Time wounds all heels

this reply: 12 points (with 2 Olaaa!! Perrrfect answer.

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