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Question
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
Options
8
10
12
13
Solution
In the given problem, we have to find the value of `x- 1/x`
Given `x^2 + 1/x^2 = 102`
We shall use the identity `(a-b)^2 = a^2 + b^2 - 2ab`
Here putting`x^2 + 1/x^2 = 102`,
`(x-1/x)^2 = x^2 + 1/x^2 - 2 (x- 1/x)`
`(x-1/x)^2 =102 - 2(x xx 1/x)`
`(x- 1/x)^2 = 102 -2`
`(x- 1/x)^2 = 100`
`(x-1/x) xx (x - 1/ x) = 10 xx 10`
`(x-1/x) = 10`
Hence the value of `x-1/x`is 10 .
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