If x^p = y^q = (xy)^pq , show that p+q = 1

Asked by sinhayashvi90 | 23rd Jun, 2022, 10:53: PM

Expert Answer:

Hint straight x to the power of straight p equals straight k straight x equals left parenthesis straight k right parenthesis to the power of 1 divided by straight p end exponent space straight y equals left parenthesis straight k right parenthesis to the power of 1 divided by straight q end exponent space space left parenthesis xy right parenthesis to the power of pq space space equals space straight k open parentheses left parenthesis straight k right parenthesis to the power of 1 divided by straight p end exponent cross times left parenthesis straight k right parenthesis to the power of 1 divided by straight q end exponent close parentheses to the power of pq space equals straight k open parentheses left parenthesis straight k right parenthesis to the power of 1 over straight p plus 1 over straight q end exponent close parentheses to the power of pq equals straight k open parentheses left parenthesis straight k right parenthesis to the power of fraction numerator straight p plus straight q over denominator pq end fraction end exponent close parentheses to the power of pq equals straight k this space gives comma straight p plus straight q equals 1

Answered by  | 24th Jun, 2022, 01:37: AM

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