If $x^2+y^2 \leq 1$, then $|x+y|\leq 1$?
It's probably very easy, but I can't solve it : )
It's a part of bigger problem.
I have to do this one: I know that $x^2+y^2 \leq 1$. I must find a smallest number n which fulfills $|x+y|+|x-y|\leq n$. It's probably $2$, but I don't know how to show that.
I know that $|x| \leq 1$, $|y| \leq 1$. It's easy to show that $|x+y|+|x-y| \leq |x|+|y|+|x|+|y| \leq 4$.
But how to get $2$.