Question

if a=2+root3 then find a-1/a

Answer 1

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

Answer 2

the ans of your question is 2√3