Question

√3-1
______. =a+ b √3find a and b
√3 +1

Answer 1

Answer:

$\implies \dfrac{\sqrt3 - 1}{\sqrt3 + 1}$

Multiply as well as divide by √3 - 1 :

$\implies \dfrac{\sqrt3 - 1}{\sqrt3 + 1}\times \dfrac{\sqrt3 -1}{\sqrt3 - 1} \\\\\\\implies\dfrac{(\sqrt3 - 1)^2}{(\sqrt3 - 1)(\sqrt3 + 1)}$

For numerator: ( a + b )² = a² + b² + 2ab

For denominator: ( a + b )( a - b ) = a² - b²

$\implies\dfrac{3+1-2\sqrt3}{(\sqrt3)^2 -1^2}\\\\\\\implies\dfrac{4-2\sqrt3}{3-1}\\\\\\\implies \dfrac{2(2-\sqrt3)}{2}\\\\\\\implies 2-\sqrt3$

Comparing values

a + b√3 = 2 - √3

a = 2 and b = - 1