# If (√3-1)/(√3+1)=a+b√3, then the value of a and b is :

(a) 3,5

(b) 4, -3

(c) 2, -1

(d) 7, 3

**Answer: (c) 2, -1**

**Solution:-**

(sqrt.3 – 1)/(sqrt.3 + 1) = a + b sqrt.3

Taken, L H S.

(sqrt.3 – 1) (sqrt.3 – 1) /(sqrt.3 + 1) (sqrt.3 – 1)

= (sqrt.3 – 1)^2/(3 – 1)

= {(sqrt.3)^2 + (1)^2) – 2 x sqrt.3 x 1}/2

= (3 + 1 – 2 sqrt.3)/2

= 4/2 – 2 sqrt.3/2

= 2 – sqrt.3

Then, 2 – sqrt.3 = a + b sqrt.3

Comparing on both side,

a = 2 & b = -1,

So, the value of a & b are 2 & -1.

Hence, the correct answer is option (c) 2, -1.