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solve for x and y

and x^x + y^y = 31

i have found x,y = 2,3 or 3,2
but i got the answer by merely substituting the values...
is there any proper way to find x and y??

  • equations -

    this equation is not easily to solve algebraically.

    x^x + (5-x)^(5-x) = 31

    can't take logs, or roots, or anything easy. Not sure what doing this kind of exercise is intended to teach.

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