Question

Find the value of a and b if ,
√3-1 / √3+1=a-b√3

Answer 1

Hey friend, here you go-

Given: $\frac{\sqrt{3}-1 }{\sqrt{3}+1 } =a+b\sqrt{3}$

To find: The values of a and b

Solution: By rationalizing the denominator,

$\frac{\sqrt{3}-1 }{\sqrt{3}+1 }*\frac{\sqrt{3}-1 }{\sqrt{3}-1 } =a+b\sqrt{3}$

By applying identities (a-b)^2=a^2+b^2-2ab and a^2-b^2=(a+b)(a-b),

$\frac{\sqrt{3}^{2} +1^{2} -2\sqrt{3} }{\sqrt{3}^{2} -1^{2} } =a+b\sqrt{3}$

$\frac{4-2\sqrt{3} }{2} = a+b\sqrt{3}$

By comparison, a=2 and b= -1

Hope this helps you..

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