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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 - 1/x)^2 = "y"^2`
`x^2 + 1/x^2 -2 = y^2`
`=> x^2 + 1/x^2 = y^2 + 2`
m2 + 2 - 3(m) - 2 = 0
m2 - 3m = 0
m (m - 3) = 0
m = 0 and m - 3 = 0
`x - 1/x = 0 or x - 1/x=3`
`(x^2-1)/x=0 or (x^2-1)/x=3`
= x2 - 1 = 0 or x2 - 1 = 3x
x2 = 1 or x2 - 3x - 1 = 0
x = `sqrt1 or x = (-(-3)±sqrt((-3)^2-4(1)(-1)))/(2(1))`
x = ± 1 or = x = `(3±sqrt13)/2`
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