# Math Help - triangle inequality

1. ## triangle inequality

How do I prove the following identity?

| |x| -|y| | <= |x - y|

Thank you

2. Originally Posted by PersaGell
How do I prove the following identity?

| |x| -|y| | <= |x - y|

Thank you
$|xy|\geq xy$

$-2|x||y|\leq -2xy$

$x^2-2|x||y|+y^2 \leq x^2 - 2xy + y^2$

$0 \leq (|x|-|y|)^2 \leq (x-y)^2$

$\sqrt{(|x|-|y|)^2} \leq \sqrt{(x-y)^2}$

$||x|-|y||\leq |x-y|$

3. Here is a second way.