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If x = √3 + 1/ √3 - 1 and y = √3 - 1/ √3 + 1, then x2 + y2 is equal to
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- 14
- 13
- 15
- 10
Correct Option: A
You can square the both the equation and add them to find the answer.
x2 + y2 = ( (√3 + 1 ) / ( √3 - 1 ) )2 + ( (√3 - 1 ) / (√3 + 1) )2
x2 + y2 = ( √3 + 1 )2 / ( √3 - 1 ) 2 + (√3 - 1 )2 / (√3 + 1) 2
x2 + y2 = ( ( 3 + 1 + 2 √3 ) / ( 3 + 1 - 2 √3 ) ) + ( ( 3 + 1 - 2√3) / ( 3 + 1 + 2 √3 ) )
x2 + y2 = ( 4 + 2 √3 ) / ( 4 - 2 √3 ) + ( 4 - 2√3 ) / ( 4 + 2 √3 )
x2 + y2 = ( 2 + √3 ) / ( 2 - √3 ) + ( 2 - √3 ) / ( 2 + √3 )
x2 + y2 = (4 + 3 + 4 √3 + 4 + 3 - 4 √3) / ( 4 - 3 )
x2 + y2 = 14
