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Question
If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`
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Solution
`(x - 1/x)^2 = x^2 = 1/x^2 - 2 xx x xx 1/x`
`(x - 1/x)^2 = x^2 + 1/x^2 - 2`
`=>(x - 1/x)^2 = 66 - 2` [∵ `x^2 + 1/x^2 = 66`]
`=> (x - 1/x)^2 = 64`
`=> (x - 1/x)^2 = (+-8)^2`
`=> x - 1/x = +-8^2`
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