Proving |X + Y|² + |X - Y|² = 2|X|² + 2|Y|²

EvLer · Apr 19, 2005

In one of my homework problems we are asked to prove this:

|X + Y|^2 + |X - Y|^2 = 2|X|^2 + 2|Y|^2

It seems quite simple: I just expanded both of them (cancelled 2(X dot Y) terms) and came up with the expression on the right. Is there something I am missing or is it really that simple?

Thanks !

Hurkyl · Apr 19, 2005

It really is!

mathwonk · Apr 19, 2005

linear algebra makes many questions in geometry rather trivial. for this reason high schools should teach the subject, instead of calculus, where they usually do an extremely bad job.

Proving |X + Y|² + |X - Y|² = 2|X|² + 2|Y|²

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Proving |X + Y|² + |X - Y|² = 2|X|² + 2|Y|²

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