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Question
If `x = sqrt(2) + 1`, find `x - 1/x`.
Sum
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Solution
Given: `x = sqrt(2) + 1`
Step-wise calculation:
1. Calculate `1/x`:
`1/x = 1/(sqrt(2) + 1)`
= `1/(sqrt(2) + 1) xx (sqrt(2) - 1)/(sqrt(2) - 1)`
= `(sqrt(2) - 1)/((sqrt(2))^2 - 1^2)`
= `sqrt(2) - 1`
2. Find `x - 1/x`:
`x - 1/x = (sqrt(2) + 1) - (sqrt(2) - 1)`
= `sqrt(2) + 1 - sqrt(2) + 1`
= 2
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Chapter 1: Rational and Irrational Numbers - Exercise 1E [Page 32]
