# Why is the following true ?!!

• May 20th 2012, 09:56 PM
howdigethere
Why is the following true ?!!
Sorry to have to ask this, but I am stuck...

Why is this true:

$2\left| x_1 x_2 \right| \leq x_1^2 + x_2^2$

???

How do I reach that conclusion from:

$(x_1 + x_2)^2 = x_1^2 + x_2^2 + 2x_1x_2$

???

• May 21st 2012, 01:12 AM
emakarov
Re: Why is the following true ?!!
Quote:

Originally Posted by howdigethere
How do I reach that conclusion from:

$(x_1 + x_2)^2 = x_1^2 + x_2^2 + 2x_1x_2$

Not only $(x_1 + x_2)^2\ge0$, but also $(x_1 - x_2)^2\ge0$. And either $-2x_1x_2=|x_1x_2|$ or $2x_1x_2=|x_1x_2|$.
• May 21st 2012, 01:34 AM
howdigethere
Re: Why is the following true ?!!
dang.

Thank You emakarov!