Question

1. If x= 2 + /3 , Find the value of a -1/a​

Answer 1

✰ Correct Question ✰

If a = 2 + √3 then find the value of a-1/a

✰ Solution ✰

• a = 2 + √3 ---(i)

✑ Rationalize

→ 1/a = 1/2 + √3 × 2 - √3/2 - √3

✑ Applying identity : a² - b² = (a+b)(a - b)

→ 1/a = 2 - √3/(2)² - (√3)²

→ 1/a = 2 - √3/4 - 3

→ 1/a = 2 - √3 ---(ii)

✑ From (i) and (ii)

→ a - 1/a

→ 2 + √3 - (2 - √3)

→ 2 + √3 - 2 + √3

→ √3 + √3

→ √3(1 + 1)

→ 2√3

Hence, the value of a - 1/a is 2√3