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The sum of square of two numbers is equal to 5 times their sum. The sum of the reciprocals of the squares of these two numbers is equal to 5/18 times the sum of the reciprocals of the given numbers. Find these numbers.
Asked by vikasg13.hardware | 07 Aug, 2018, 05:37: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight x squared plus straight y squared equals 5 1 over straight x squared plus 1 over straight y squared equals 5 over 18 fraction numerator straight x squared plus straight y squared over denominator straight x squared straight y squared end fraction equals 5 over 18 fraction numerator 5 over denominator straight x squared straight y squared end fraction equals 5 over 18 straight x squared straight y squared equals 18 xy equals square root of 18 open parentheses 1 over straight x plus 1 over straight y close parentheses squared minus 2 1 over xy equals 1 over straight x squared plus 1 over straight y squared open parentheses 1 over straight x plus 1 over straight y close parentheses squared equals 1 over straight x squared plus 1 over straight y squared plus 2 over xy open parentheses 1 over straight x plus 1 over straight y close parentheses squared equals 5 over 18 plus fraction numerator 2 over denominator square root of 18 end fraction equals fraction numerator 5 square root of 18 plus 36 over denominator 18 square root of 18 end fraction 1 over straight x plus 1 over straight y equals square root of fraction numerator 5 square root of 18 plus 36 over denominator 18 square root of 18 end fraction end root end style
Answered by Arun | 08 Aug, 2018, 12:23: PM

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