Question

If a = 6+2√5 find the value of a-1/a​

Answer 1

a = 6 + 2√5

a - 1/a

• Solving 1/a = 1 / 6 + 2√5

Rationalising the denominator

6 - 2√5 / (6)² - (2√5)²

6 - 2√5 / 36 - 20

6 - 2√5 / 16

2 ( 3 - √5 ) / 2 x 8

3 - √5 / 8

• Now a - 1/a = 6 + 2√5 - ( 3 - √5 ) / 8

{ 8 ( 6 + 2√5 ) - ( 3 - √5 ) } / 8

( 48 + 16√5 - 3 + √5 ) / 8

45 + 17√5 / 8 ➡ Answer