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Question
Solve:
`(x^2 + 1/x^2) - 3(x - 1/x) - 2 = 0`
Solution
`(x^2 + 1/x^2) - 3(x - 1/x) - 2 = 0`
Let `x - 1/x = y`
Squaring on both sides
`x^2 + 1/x^2 - 2 = y^2`
`=> x^2 + 1/x^2 = y^2 + 2`
Putting these values in the given equation
(y2 + 2) – 3y – 2 = 0
`=>` y2 – 3y = 0
`=>` y(y – 3) = 0
If y = 0 or y – 3 = 0
Then y = 0 or y = 3
`=> x - 1/x = 0` or `x - 1/x = 3`
`=> (x^2 - 1)/x = 0` or `(x^2 - 1)/x = 3`
`=> x^2 - 1 = 0` or `x^2 - 3x - 1 = 0`
`=> (x + 1)(x - 1) = 0` or `(-(-3) +- sqrt((-3)^2 - 4(1)(-1)))/(2(1))`
`=> x = -1` and `x = 1` or `x = (3 +- sqrt13)/2`
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