Question 1087653
{{{ highlight( a^2 + b^2  = ab(a+b) )}}}     ; a,b both positive integers 

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To see the answer is equivalent to the original, (since a>0 & b>0)  divide  both sides by ab to get back to the original:

{{{  (a^2 + b^2)/(ab) = ab(a+b)/(ab) }}}
{{{   a/b + b/a  =  a+b }}} 

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Edit 7/15/17:  Edwin is right, I just thought you wanted an alternate form of {{{a^2+b^2}}} in terms of a & b.