Question

In the following, find the value of a and b:

`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`

Answer 1

`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1)`

= `(sqrt(3) - 1)/(sqrt(3) + 1) xx (sqrt(3) - 1)/(sqrt(3) - 1) + (sqrt(3) + 1)/(sqrt(3) - 1) + (sqrt(3) + 1)/(sqrt(3) + 1)`

= `(sqrt(3) - 1)^2/((sqrt(3))^2 - 1) + (sqrt(3) + 1)^2/((sqrt(3))^2 - 1)`

= `((sqrt(3))^2 - 2 xx sqrt(3) xx 1 + 1^2)/(3 - 1) + ((sqrt(3))^2 + 2 xx sqrt(3) xx 1 + 1^2)/(3 - 1)`

= `(3 - 2sqrt(3) + 1)/(2) + (3 + 2sqrt(3) + 1)/(2)`

= `(4 - 2sqrt(3))/(2) + (4 + 2sqrt(3))/(2)`

= `(2(2 - sqrt(3)))/(2) + (2(2 + sqrt(3)))/(2)`

= `2 - sqrt(3) + 2 + sqrt(3)`
= 4 + 0
Hence, a = 4 and b = 0