# Math Help - Abstract Inequalities

1. ## 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 $a^2+4ab+4b^2\geq0$?

2. ## Re: Abstract Inequalities

Originally Posted by GrigOrig99
Q. [/B]Prove $a^2+2ab+2b^2\geq0$
$(a+b)^2+b^2\ge 0~.$

3. ## Re: Abstract Inequalities

Ok, thank you.