Easy identity

by shiningsunnyday, Oct 18, 2016, 11:25 AM

Well-known / 105 Algebra Problems wrote:
Prove that $$(x_1^2+x_2^2+ \ldots + x_n^2)(y_1^2+y_2^2+ \ldots + y_n^2) = (x_1y_1 + x_2y_2 + \ldots + x_ny_n)^2 + \sum_{1 \le i < j \le n} (x_iy_j - x_jy_i)^2.$$
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This post has been edited 1 time. Last edited by shiningsunnyday, Oct 18, 2016, 11:27 AM

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wow nice proof of cauchy :D

Thanks
This post has been edited 1 time. Last edited by shiningsunnyday, Oct 21, 2016, 8:27 AM

by MathStudent2002, Oct 18, 2016, 11:40 PM

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I feel like the above is tautological (or at least really easy) O wait that's why it's called easy lol.

by FlyingCucumber, Oct 19, 2016, 3:08 AM

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Because the expansion just happens to work that way.

by FlyingCucumber, Oct 19, 2016, 3:09 AM

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(FC's humble brag)

D:
This post has been edited 1 time. Last edited by shiningsunnyday, Oct 21, 2016, 8:28 AM

by zephyrcrush78, Oct 19, 2016, 4:01 AM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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