If $a^b = b^a$ and $a=2b$ then find the value of $a^2+b^2$ If $a^b = b^a$ and $a=2b$ then find the value of $a^2+b^2$
My Attempt, 
$$a^b = b^a$$
$$a^b =b^{2b}$$
$$a^b =b^b.b^b$$.
Now, what should I do further? 

Continue from your solution -
$a = (b^{2b})^{\frac 1b}$
$a = b^2$
Also a = 2b.
So we have,
$b^2 = 2b$
Assuming b is real positive number.
b = 2.
a = 4.
