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Question
If `x = 2 + sqrt(3)`, find `x - 1/x`.
Sum
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Solution
Given: `x = 2 + sqrt(3)`
Step-wise calculation:
1. First, find `1/x`:
`1/x = 1/(2 + sqrt(3)) xx (2 - sqrt(3))/(2 - sqrt(3))`
= `(2 - sqrt(3))/((2)^2 - (sqrt(3))^2`
= `(2 - sqrt(3))/(4 - 3)`
= `2 - sqrt(3)`
2. Now calculate `( x - 1/x)`:
`x - 1/x = (2 + sqrt(3)) - (2 - sqrt(3))`
= `2 + sqrt(3) - 2 + sqrt(3)`
= `2sqrt(3)`
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Chapter 1: Rational and Irrational Numbers - Exercise 1E [Page 32]
