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Question
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
Solution
We have to find the value of `x^2 + 1/x^2 `
Given `x+ 1/x = 3`
Using identity `(a+b)^2 = a^2 + 2ab + b^2`
Here `a= x,b= 1/x`
`(x+1/x)^2 = x^2 + 2 xx x xx 1/x + (1/x)^2`
`(x+1/x)^2 = x xx x +2 xx x xx 1/x + 1/x xx 1/x`
` (x+1/x)^2 = x^2 + 2+ 1/x^3`
By substituting the value of `x + 1/x = 3` we get,
`(3)^2 = x^2 + 2+ 1/x^2`
`3 xx 3 = x^2 + 2 +1/x^2`
By transposing + 2 to left hand side, we get
`9 -2 = x^2 +1/x^2`
`7 = x^2 + 1/x^2`
Hence the value of `x^2 + 1/x^2`is 7 .
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