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Question
If x = `sqrt(7) - 2`, find the value of `(x + 1/x)`.
Solution
Given: x = `sqrt(7) - 2`
⇒ `1/x = 1/(sqrt(7) - 2)`
= `1/(sqrt(7) - 2) xx (sqrt(7) + 2)/(sqrt(7) + 2)`
= `((sqrt(7) + 2))/((sqrt(7) - 2)(sqrt(7) + 2))`
= `((sqrt(7) + 2))/((sqrt(7))^2 - (2)^2) = ((sqrt(7) + 2))/(7 - 4)`
= `((sqrt(7) + 2))/3`
Now, `(x + 1/x) = sqrt(7) - 2 + ((sqrt(7) + 2))/3`
= `(3sqrt(7) - 6 + sqrt(7) + 2)/3`
= `(4sqrt(7) - 4)/3`
Hence, the value of `(x + 1/x)` is `(4sqrt(7) - 4)/3`.
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