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

Posted by Sumit Sarkar 8 years, 3 months ago

CBSE > Class 09 > Mathematics

2 answers

Rashmi Bajpayee 8 years, 3 months ago

{tex}a + b = {a \over b} + {b \over a}{/tex}

=> {tex}a + b = {{{a^2} + {b^2}} \over {ab}}{/tex}

=> {tex}{a^2} + {b^2} = ab\left( {a + b} \right){/tex}

0Thank You

Hans Raj 8 years, 3 months ago

a + b = a/b + b/a

squaring both sides

a² + b² + 2ab = a²/b² + b²/a² + 2

a² + b² = a²/b² + b²/a² + 2 - 2ab

0Thank You

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CBSE > Class 09 > Mathematics