Question

find the value of x and y of √3-1 / √3+1= x+y√3​

Answer 1

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Answer 2

$\frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1} = x + y \sqrt{3}$

Taking LHS

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

Multiply Numerator and Denominator by √3-1

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

Hence, x = 2 and y = - 1