Question

x^Y=y^x and Y=x^2 find x and y

Answer 1

Given,

x^y=y^x. equa. (1)

And, y=x^2

By putting y=x^2 in equation (1)

We have ,

x^x^2=x^2x

By comparison,

x^2=2x

so either x=2 or 0.

so by putting x=2 or 0

we will get

y=4 or 0