Is the equality (x + y)^2 = O(x^2 + y^2) true?

Question

Mathematics

Is this equality true, and how is it proved?

Answer 1

Не верно. Очевидно. Потому что 2xy = O(1)
Пусть C = 3
Докажем, что (x + y)^2 <= 3 * (x^2 + y^2) при x > 0 и y > 0:
после преобразований 2*x*y <= 2*x^2 + 2*y^2
Если x < y, то 2*x*y < 2*y^2
Если x >= y, то 2*x*y <= 2*x^2
ч.т.д.

Answer 2

Well, if x=0 and y = 0 It's
definitely true )
--
Too lazy to look at other values.... and it's not clear there O(....) or 0(.....) ?