Question

If $x^y=y^x$ and $x=2y$, then find the value of x+y. (Assume that $y\ne 0$)

Answer 1

$x^y=y^x$ & $x=2y$

$\Rightarrow (2y{)}^y=y^{2y}\Rightarrow 2^y{y}^y=(y^y{)}^2$

$\Rightarrow 2^y=y^y\Rightarrow y=2\therefore x=4$

$\Rightarrow x+y=6$