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Question
If `a = 2 + sqrt(3)`, then find the value of `a - 1/a`.
Solution
Given that `a = 2 + sqrt(3)`,
∴ We have `1/a = 1/(2 + sqrt(3))`
⇒ `1/a = 1/(2 + sqrt(3)) xx (2 - sqrt(3))/(2 - sqrt(3))` ...[Using (a – b)(a + b) = a2 – b2]
⇒ `1/a = (2 - sqrt(3))/(4 - 3)`
⇒ `1/a = 2 - sqrt(3)`
Now ` a - 1/a = 2 + sqrt(3) - (2 - sqrt(3))`
⇒ `a - 1/a = 2sqrt(3)`
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