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Question
If a=,2+, root3 then find the value of a-1/a
If a=,2+, root3 then find the value of a-1/a
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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)
= 2+√3-2+√3
= 2√3
Answer : a-1/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)
= 2+√3-2+√3
= 2√3
Answer : a-1/a = 2√3
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