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# If √ 3 − 1 √ 3 + 1 = a − B √ 3 Then - Mathematics

MCQ

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

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#### Solution

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

Is there an error in this question or solution?
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Q 6 | Page 17
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