Question

√3-1\√3+1 = a-b√3. find the value of a and b.

Answer 1

Hey friend,

Here is your answer,
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√3 - 1  
√3 + 1

=> (√3-1)(√3-1)
     (√3+1)(√3-1)

=> 3+1-2√3
         3-1

=> 4 - 2√3
         2

=> 2 - √3


2 - √3  =  a - b√3
a = 2        b = 1

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Answer 2

√3-1\√3+1=a-b√3
(Rationalize the denominator)
In LHS(left hand side)
= (√3-1)(√3-1)\(√3+1)(√3-1)
= 3+1-2√3\3-1
=4-2√3\2
(Taking 2 common from numerator)
=2-√3 (1)
In RHS
a-b√3. (2)
A.T.Q(according to question)
(1)=(2)
2-√3=a-b√3 (Comparing both equations)
So, a=2,b=1.