SOLUTION: Solve for x and y; √(x)^√(y) + √(y)^√(x) = 145

Algebra.Com
Question 1209508: Solve for x and y;
√(x)^√(y) + √(y)^√(x) = 145
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20081)   (Show Source): You can put this solution on YOUR website!




That's got variables both inside and not inside exponents in more
than 1 term, So very likely, algebra is useless.  Besides that, there 
are two variables, but only one equation.  So there are no doubt 
infinitely many solutions.

Using a TI-84 graphing calculator,
one approximate solution is 

x = y = 11.93702491

You can find plenty of other approximate solutions, by making up 
values for y and solving for x with your TI-84.

Edwin
Answer by ikleyn(53763)   (Show Source): You can put this solution on YOUR website!
.

As Edwin explained in his post, this equation has infinitely many solutions in real numbers,
therefore the problem's request, as it is given in the post, makes no sense.

The problem gets sense, if to ask about solutions in integer positive numbers.

Notice that

        145 = 81 + 64 = 64 + 81,

    or

        145 = + = + .

It gives two solutions in integer positive numbers

        (a)   x = 9, y = 16;

        (b)   x = 16, y = 9.


There are other solutions. Consider this decomposition

        145 = 144 + 1 = 1 + 144.


It gives two more solutions in integer numbers

        (c)   x = , y = 1;

        (d)   x = 1, y = .



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