Question

How to prove:
\(||x+y||||x-y||\leq ||x||^2 +||y||^2\)
Please, help

Answer 1

Triangle inequality shows:
\[||x+y||\leq||x||+||y||\]
But I don't know the case ||x -y||

Answer 2

mood up, right? hihihi

Answer 3

|x-y| |x+y|=|x^2-y^2|

this should work

Answer 4

|x^2-y^2| <=|x^2+y^2|<=|x^2|+|y^2|

Answer 5

It works, but we have to use inequality theorem to show, friend, or Cauchy Schwarz

Answer 6

triangle is enough i guess

Answer 7

ok, it works,:) thank you, friend

Answer 8

wait , but what if u prof want it as what u said ?
u cant close the question :O

Answer 9

why not? it makes sense to me,now
I can use it as you said, clearly, |x|^2 -|y|^2 < |x|^2+|y|^2

Answer 10

and the left hand side satisfies the triangle inequality,
We just make them link by skipping the middle term.

Answer 11

yep ^^