Question

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

Answer 1

ANSWER:

• Value of a = 2.
• Value of b = 1.

GIVEN:

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

TO FIND:

• Value of a and b.

SOLUTION:

$= \dfrac{ \sqrt{3} - 1 }{ \sqrt{3} + 1} \\ \\ = \dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1 } \\ \\ = \dfrac{( \sqrt{3} - 1) {}^{2} }{3 - 1} \\ \\ = \dfrac{4 - 2 \sqrt{3} }{2} \\ \\ = \dfrac{2(2 - \sqrt{3} )}{2} \\ \\ \implies \: 2 - \sqrt{3} = a - b \sqrt{3} \\ \\ here \: a \: = \: 2 \: \: \: and \: \: \: \: b = 1$

Value of a = 2.

Value of b = 1.