Question

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

Answer 1

Answer:

a = 2 and b = -1

Step-by-step explanation:

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

To find: vale of a & b

We find value of a & b by rationalizing the denominator of LHS and then equating with RHS

Consider,

LHS

=\frac{\sqrt{3}-1}{\sqrt{3}+1}

=\frac{\sqrt{3}-1}{\sqrt{3}+1}\times\frac{\sqrt{3}-1}{\sqrt{3}-1}

=\frac{(\sqrt{3}-1)^2}{(\sqrt{3}+1)(\sqrt{3}-1)}

=\frac{(\sqrt{3})^2+(1)^2-2\sqrt{3}}{(\sqrt{3})^2-(1)^2}

=\frac{3+1-2\sqrt{3}}{3-1}

=\frac{4}{2}-\frac{2\sqrt{3}}{2}

=2-\sqrt{3}

Now equating with RHS = a + b√3

we get a = 2 7  b = -1

Therefore, a = 2 and b = -1