Question

if a= 6+2√3 then Find the value of a-1/a

Answer 1

Given a = 6 + 2√3

⇒ (1/a) = 1 / (6+ 2√3)

Multiply and divide by (6 − 2√3)

⇒ (1/a) = (6 − 2√3) / [(6 +2√3)(6 − 2√3)]

⇒ (1/a) = (6 − 2√3) / [36 − 12]

⇒ (1/a) = (6 − 2√3) /24

∴ a-1/a

→ (6+2√3) - (6-2√3)/24

→ {24(6+2√3) - 6 + 2√3}/24

→ {144+48√3-6+2√3}/24

→ {138+50√3}/24

→ 138/24 + 50√3/24

→ 69/12 + 25√3/12

→ {69+25√3}/12

Answer : {69+25√3}/12