Question

What is the value of a and B in the equation √3 - 1/ √3+1 = a-b3​

Answer 1

Step-by-step explanation:

$\frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1 } = a - b \sqrt{3} \\ \\ \frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1} = \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1 } \times \frac{ \sqrt{3} - 1 }{ \sqrt{3} - 1} \\ = \frac{ {( \sqrt{3} - 1) }^{2} }{( \sqrt{3} + 1)( \sqrt{3} - 1)} \\ = \frac{3 - 2 \sqrt{3} + 1}{ ({ \sqrt{3}) }^{2} - 1} \\ = \frac{4 - 2 \sqrt{3} }{3 - 1} \\ = \frac{4 - 2 \sqrt{3} }{2} \\ = \frac{2(2 - \sqrt{3}) }{2} = 2 - \sqrt{3}$

Therefore, a=2 , b =1