Question

If x is root 5 plus 2 find x-1/x

Answer 1

Answer:

$x = \sqrt{5} + 2 \\ \frac{1}{x} = \frac{1}{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2 }{ \sqrt{5} - 2} \\ \frac{1}{x} = \frac{ \sqrt{5} - 2}{5 - 4} = \frac{ \sqrt{5} - 2 }{1} = \sqrt{5} - 2 \\ therefore \ \: :x - \frac{1}{x} = \sqrt{5} + 2 - \sqrt{5 } + 2 \\ = x + \frac{1}{x} = 2 + 2 = 4$