Question

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

Answer 1

Answer:

• The value of x and y is 2 and -1 respectively.

Step-by-step explanation:

Given,

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

To Find,

• The value of x and y.

Solution,

$:\implies \tt\frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} = x + y \sqrt{3} \\ \\ :\implies \tt \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1} = x + y \sqrt{3} \\ \\ :\implies \tt \frac{ {( \sqrt{3} - 1)}^{2} }{ {( \sqrt{3}) }^{2} - {(1)}^{2} } = x + y \sqrt{3} \\ \\ :\implies \tt \frac{{( \sqrt{3 } )}^{2} - 2(1)( \sqrt{3}) + {1}^{2} }{3 - 1} = x + y \sqrt{3} \\ \\ :\implies \tt \frac{3 - 2 \sqrt{3} + 1 }{2} = x + y \sqrt{3} \\ \\ :\implies \tt \frac{4 - 2 \sqrt{3} }{2} = x + y \sqrt{3} \\ \\ :\implies \tt \frac{2(2 - \sqrt{3}) }{2} = x + y \sqrt{3} \\ \\ :\implies \tt 2 - \sqrt{3} = x + y \sqrt{3} \\ \\ :\implies \color{red} \boxed{x = 2} \: \: \: \: and \: \: \: \boxed{y = - 1}$

Required Answer,

• The value of x and y is 2 and -1 respectively.