# Abstract Inequalities

• October 18th 2012, 08:37 AM
GrigOrig99
Abstract Inequalities
Having a bit of trouble with this one. Can anyone help?

Many thanks.

Q.
Prove $a^2+2ab+2b^2\geq0$

Attempt: My original solution was going to be...: if $(a+b)(a+2b)\geq0$

However, this does not fit the format of (real no.)2 > 0

The alternative method I've found goes as follows: $a^2+2ab+2b^2\geq0$
if $a^2+4ab+4b^2\geq0$
if $(a+b)^2$...true, since (a+b)2 > 0

Is this 2nd approach correct? How did they go from $a^2+2ab+2b^2\geq0$ to $a^2+4ab+4b^2\geq0$?
• October 18th 2012, 10:05 AM
Plato
Re: Abstract Inequalities
Quote:

Originally Posted by GrigOrig99
Q. [/B]Prove $a^2+2ab+2b^2\geq0$

$(a+b)^2+b^2\ge 0~.$
• October 18th 2012, 10:09 AM
GrigOrig99
Re: Abstract Inequalities
Ok, thank you.