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Question
QUESTION: Solve:
a+b = 5
(a^b)+(b^a) = 17

ANS.  a=2, b=3

ANSWER: You sent me a problem and the answer, what it is that you want?

---------- FOLLOW-UP ----------

QUESTION: I want the solution without hit & trial method.

Thanks in Advance.

Answer
I don't believe there is any way to get a closed form for the answer. For example a simpler problem is to just solve an equation like a^a=17. You might find the article here interesting:

http://mathforum.org/library/drmath/view/70483.html

In your problem you are intersecting a line with a strange curve, there's no reason to expect a "nice" answer for a and b.

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