Math, asked by subhashpantha9, 3 months ago

if x^a.x^b=(x^a)^b prove that a/b +b/a =ab-2​

Answers

Answered by mvandana542
0

Answer:

It suffices to prove it for x=e because then xaxb=ealnxeblnx=e(a+b)lnx=xa+b.

eaeb=∑n=0∞ann!∑n=0∞bnn!=∑n=0∞∑k=0nakk!bn−k(n−k)!=∑n=0∞∑k=0n1n!(nk)akbn−k=∑n=0∞(a+b)nn!=ea+b

Here we use Cauchy's product formula, the series converge absolutely.

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