Question

If √3 - 1 / √3 + 1 = a – b√3, then
A. a = 2, b = 1
B. a = 2, b = -1
C. a = -2, b = 1
D. a = b = 1

Answer 1

Answer: a

Steps in attachment

Answer 2

Given :  √3 - 1 / √3 + 1 = a – b√3

We have , √3 - 1 / √3 + 1

On rationalising the denominator :

= (√3 - 1) (√3 - 1)/ (√3 + 1)(√3 - 1)

= (√3 - 1)²/√3² - 1²

[By using an identity, (a + b) (a - b) = a² - b²]

= √3² + 1² - 2 × √3 × 1 / (3 - 1)

[By using an identity,(a – b)² = a² + b² – 2ab]

= (3 + 1 - 2√3)/2

= (4 - 2√3)/2

= 4/2 - 2√3/2

√3 - 1 / √3 + 1 = 2 - √3  

Now,  

√3 - 1 / √3 + 1 = a – b√3

2 - √ 3 = a – b√3

On Comparing , we obtain  

a = 2 , b = 1

Hence the value of  a is 2 and b is 1.

Among the given options option (A) a = 2, b = 1  is correct.

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