Abstract Inequalities

**GrigOrig99** · October 18th 2012, 08:37 AM

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 $a^2+4ab+4b^2\geq0$ ?