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Question

The sum of positive number and its reciprocal is thrice  the difference of the number and its reciprocal

The number is:


Options:
A .  `sqrt(2)`
B .  `1/sqrt(2)`
C .  `sqrt(3)`
D .  `1/sqrt(3)`
Answer: Option A

Let the number be  `x`. Then ,

`x + 1/x` =  `3(x - 1/x)`  `hArr`  `(x^2 + 1)/(x)` =  `3((x^2 - 1)/(x))`

`hArr`  `x^2 + 1` = `3x^2 - 3`  `hArr`   `2x^2` = 4  `hArr`  `x^2` = 2  `hArr`  `x`  = `sqrt(2)`



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