Question

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

Answer 1

Answer:

a - 1/a is  (6 + 4√3)/(2 +√3)

Step-by-step explanation:

a = 2+ √3

a - 1/a

(2 + √3) - 1/(2 + √3)

Take LCM

[(2 +√3)(2 + √3) - 1]/(2 + √3)

= [(2 + √3)² - 1]/(2 + √3)

= (4 + 3 + 4√3 - 1)/(2 + √3)

= (6 + 4√3)/(2 +√3)