If √3 - 1/√3 + 1 = x + y √3, find the values of x and y.

Question

If \(\frac{\sqrt3-1}{\sqrt3+1}\) = x + y √3, find the values of x and y.

Answer 1

Given, \(\frac{\sqrt3-1}{\sqrt3+1}\) = x + y√3

= \(\frac{\sqrt3-1}{\sqrt3+1}\) x \(\frac{\sqrt3-1}{\sqrt3-1}\) = \(\frac{(\sqrt3-1)(\sqrt3-1)}{3-1}\)= \(\frac{4-2\sqrt3}{2}\) = 2 - √3

So, x = 2, y = -1