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Question
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
Options
25
10
23
27
Solution
In the given problem, we have to find the value of `x^2 + 1/x^2 `
Given `x+ 1/x = 5`
We shall use the identity `(a+b)^2 = a^2 + b^2 + 2ab`
Here put `x+1/x = 5`
`(x+1/x)^2 = x^2 +1/x^2 +2 (x xx 1/x)`
`(5)^2 = x^2 + 1/x^2 +2 (x xx 1/x)`
`25 = x^2 + 1/x^2 + 2`
`25 - 2 = x^2 +1/x^2`
`23 = x^2 + 1/x^2`
Hence the value of `x^2 + 1/x^2` is 23.
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