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Question
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
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Solution
In the given problem, we have to find `x^2 + 1/x^2`
Given `(x-1/x)=-1`
On squaring both sides we get,
`(x-1/x)^2=(-1)^2`
We shall use the identity `(x-y )^2 = x^2 - 2xy + y`
`x^2 +1/x^2 - 2 xx x xx 1/x =- 1 xx -1`
`x^2 +1/x^2 -2 =1`
`x^2 +1/x^2 = 1+2`
`x^2+1/x^2 =3`
Hence the value of ` x^2 +1/x^2`is 3 .
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