Question

If √3-1upon√3+1 =a+b√3, find the value of a and b.​

Answer 1

Identities used:

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

(a + b)(a - b) = a² - b²

Answer:

a = 2 and b = 1

Step-by-step explanation:

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

Rationalizing the denominator we get:

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

a + b√3 = 2 - √3

a = 2 and b = 1