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

Anurag Mishra Professor Asked on 3rd February 2016 in Maths.
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1 Answer(s)

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.

Anurag Mishra Professor Answered on 5th February 2016.
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