Question

If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then

Options

• a = 2, b =1

• a = 2, b =−1

• a = −2, b = 1

• a = b = 1

Answer 1

Given that:`(sqrt3 -1) / (sqrt3 +1) = a -b sqrt3`

We are asked to find a and b

We know that rationalization factor for `sqrt3+1 ` is `sqrt3-1 `. We will multiply numerator and denominator of the given expression  `(sqrt3-1)/(sqrt3 +1)`by, `sqrt3-1` to get

 `(sqrt3-1)/(sqrt3 +1) xx  (sqrt3-1)/(sqrt3 -1) = ((sqrt3)^2 +(1)^2 - 2 xx sqrt3 xx 1)/((sqrt3)^2 - (1)^2)`

`= (3+1 - 2 sqrt3)/(3-1)`

`=( 4-2sqrt3)/2`

`=2-sqrt3`

On equating rational and irrational terms, we get 

`a-bsqrt3 = 2-sqrt3`

               `=2 -1sqrt3`

Comparing rational and irrational part we get

 `a=2,b=1`