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ICSE Class 9 Answered

If (p+q)-1(p-1 + q-1) =pa  q b   , prove that a+b+2=0, when p and q are different positive primes. Please provide the solution and explanation.
Asked by cbiswajit | 24 Sep, 2018, 06:17: PM
answered-by-expert Expert Answer
(p+q)-1(p-1 + q-1) = paqb 
begin mathsize 16px style fraction numerator 1 over denominator straight p plus straight q end fraction open parentheses 1 over straight p plus 1 over straight q close parentheses equals straight p to the power of straight a straight q to the power of straight b fraction numerator begin display style 1 end style over denominator begin display style straight p plus straight q end style end fraction open parentheses fraction numerator begin display style straight q plus straight p end style over denominator begin display style pq end style end fraction close parentheses equals straight p to the power of straight a straight q to the power of straight b 1 over pq equals straight p to the power of straight a straight q to the power of straight b straight p to the power of negative 1 end exponent straight q to the power of negative 1 end exponent equals straight p to the power of straight a straight q to the power of straight b straight a equals negative 1 space and space straight b equals negative 1 Hence comma straight a plus straight b plus 2 equals space minus 1 space minus space 1 space plus 2 equals 0 end style

Answered by Yasmeen Khan | 27 Sep, 2018, 11:18: AM

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