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Thread: Sum of squares

  1. #1
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    Sum of squares

    Any hints on this?

    It appears 2x( 32+52) can be expressed as 82+ 22

    I am thinking is it the case that 2x(a2 +b2) can be expressed as a sum of two integer squares for any integers a and b?

    I can't see a way of manipulating the expression to do anything?
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  2. #2
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    Re: Sum of squares

    Ok, I think i have worked this out..

    Is it case of 2(a^2+ b^2) = (a+b)^2 + (a-b)^2 ???
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  3. #3
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    Re: Sum of squares

    Quote Originally Posted by rodders View Post
    Ok, I think i have worked this out..
    Is it case of 2(a^2+ b^2) = (a+b)^2 + (a-b)^2 ???
    Why doubt your self? Do you understand why?
    $ \begin{align*}(a+b)^2+(a-b)^2&=(a^2+2ab+b^2)+(a^2-2ab+b^2) \\&=2a^2+2b^2\\&=2(a^2+b^2) \end{align*}$

    Pick any two numbers, say $7~\&~15$. Now $7^2=49~\&~15^2=225$ also $(7+15)^2=484~\&~(1-15)^2=64$
    Does it work?
    Thanks from romsek and topsquark
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    Re: Sum of squares

    Quote Originally Posted by Plato View Post

    ... also $(7+15)^2=484~\&~(1-15)^2=64$
    Does it work?
    (7 - 15)^2 = 64
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