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Question

If A = 2 + root3  , then find A - 1/A


Solution

Given a = 2 + √3
⇒ (1/a) = 1 / (2 + √3)
Multiply and divide by (2 − √3)
⇒ (1/a) = (2 − √3) / [(2 + √3)(2 − √3)]
⇒ (1/a) = (2 − √3) / [4 − 3]
⇒ (1/a) = (2 − √3)
∴ a + (1/a) = (2 + √3) + (2 − √3)
= 4

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