SOLUTION: if a^b=b^a and a=2b then find the value of a^2+b^2

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Question 37837: if a^b=b^a and a=2b then find the value of a^2+b^2
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Okay, here goes...step by step
a^b = b^a and a = 2b
Thus by substitution
(2b)^b = b^(2b)
2^b x b^b = (b^b)^2
Now divide by b^b and get
2^b = b^b
Thus b = 2
and
a = 4