<s>[INST] 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? 
 [/INST] You didn't specify what are $a,b$ ... Integers ? positive real numbers ? ...
I will assume that $a,b$ are positive real numbers, such that $a^b=b^a$ and $a=2b$.
So we have $(2b)^b=b^{2b}$, which simplifies to $2^b=b^b$, hence $b=2$ and $a=4$.
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