Question

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

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Answer 1

Step-by-step explanation:

√3-1/√3+1=a+b√3

(√3-1)/(√3)²-1=a+b√3

3+1-2√3/3-1=a+b√3

4-2√3/2=a+b√3

2-√3=a+b√3

a=2 b=-1

Answer 2

$\huge{\underline{\underline{\purple{♡Solution→}}}}$

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

Divide and multiply by √3 - 1

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

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

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

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

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