Two positive integers a and b are such that a+b = a/b + b/a. What is the value of a square + b square

Asked by vikasg13.hardware | 13th Jun, 2018, 11:37: AM

Expert Answer:

begin mathsize 16px style straight a plus straight b equals straight a over straight b plus straight b over straight a
straight a plus straight b equals fraction numerator straight a squared plus straight b squared over denominator ab end fraction
ab open parentheses straight a plus straight b close parentheses equals straight a squared plus straight b squared
straight a squared straight b plus ab squared equals space straight a squared plus straight b squared
straight a squared straight b plus ab squared space minus space straight a squared minus straight b squared equals 0
straight a squared straight b minus space straight a squared plus ab squared minus straight b squared equals 0
straight a squared left parenthesis straight b minus 1 right parenthesis plus straight b squared left parenthesis straight a minus 1 right parenthesis equals 0
It space is space possible space only space when space straight a space equals space 1 space equals space straight b
straight a squared space plus space straight b to the power of 2 space end exponent space equals space 2 end style

Answered by Sneha shidid | 13th Jun, 2018, 03:44: PM

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