How do I prove the following identity? | |x| -|y| | <= |x - y| Thank you
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Originally Posted by PersaGell How do I prove the following identity? | |x| -|y| | <= |x - y| Thank you $\displaystyle |xy|\geq xy$ $\displaystyle -2|x||y|\leq -2xy$ $\displaystyle x^2-2|x||y|+y^2 \leq x^2 - 2xy + y^2$ $\displaystyle 0 \leq (|x|-|y|)^2 \leq (x-y)^2$ $\displaystyle \sqrt{(|x|-|y|)^2} \leq \sqrt{(x-y)^2}$ $\displaystyle ||x|-|y||\leq |x-y|$
Here is a second way.
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