Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Prove $\|x-y\|\|x+y\|\le\|x\|^2+\|y\|^2$ for all Rn

I've been struggling with this for a while and haven't figured out a way to do it either geometrically or algebraically.

share|improve this question
1  
Presumably what you mean is "for all $x$ and $y$ in ${\bf R}^n$". –  Gerry Myerson Feb 26 '13 at 0:41
    
That is correct. –  orbis Feb 26 '13 at 0:42
    
OK. Are you aware that $|x\cdot y|\le\|x\|\|y\|$? –  Gerry Myerson Feb 26 '13 at 0:43
    
Yes. Shwartz inequality. –  orbis Feb 26 '13 at 0:44
1  
OK, now that you see how to do it, write it up and post it as an answer (this site encourages people to post answers to their own questions. Then, after some time has passed, you can accept your answer by clicking in the check mark next to it. –  Gerry Myerson Feb 26 '13 at 2:03
show 3 more comments

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.