Question

Find the value of a and b
root 3 - 1 / root 3 + 1 = a + b root 3
please answer fast

Answer 1

Answer:-

a = 2

b = -1

Given :-

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

To find :-

The value of a and b.

Solution:-

$\implies$ $\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \dfrac{ \sqrt{3} - 1}{ \sqrt{3} - 1}$

$\huge \boxed {(a+b) (a-b) = a^2 -b^2}$

$\implies$ $\dfrac{( \sqrt{3} - 1) ^{2} }{( \sqrt{3})^{2} - {(1)}^{2} } = a + b \sqrt{3}$

$\implies$ $\dfrac{ { (\sqrt{3} )}^{2} + 1 - 2. \sqrt{3}.1 }{3 - 1} = a + b \sqrt{3}$

$\implies$ $\dfrac{3 + 1 - 2 \sqrt{3} }{2} = a + b \sqrt{3}$

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

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

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

By comparing,

$a = 2 \: \: b \: = - 1$