Question

√3-1/√3+1. A-b√3. Find a and b values

Answer 1

Question must be :

If (√3 - 1)/(√3 + 1) = a - b√3, find a and b

Solution :

Now,

(√3 - 1)/(√3 + 1)

= (√3 - 1)/(√3 + 1) * (√3 - 1)/(√3 - 1),

by multiplying both the numerator and the denomination by the conjugate irrational number of its denominator

= {(√3 - 1)(√3 - 1)}/{(√3 + 1)(√3 - 1)}

= (3 - √3 - √3 + 1)/(3 - √3 + √3 - 1)

= (4 - 2√3)/(2)

= 2 - √3

Given that,

    2 - √3 = a - b√3

Comparing both sides, we get

    a = 2 and b = 1

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