X^(a+b) = x^ab , prove that a/b +b/a = ab-2
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Answer:
We know that,
if x^a = x^b then,
a=b
similarly in the question
a+b = ab
RTP- a/b+b/a =ab-2
LHS- a/b + b/a = a^2+b^2/ab
=(a+b)^2-2ab/ab
=(a+b)^2/ab - 2ab/ab
=(ab)^2/ab - 2 { as a+b = ab }
=ab-2 = RHS
Hence proved
Hope it helps.
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