Question

if x - 1/ x = under root 5 find the value of x +1/x​

Answer 1

Step-by-step explanation:

x - 1/x = √5

Doing square both side

x² + 1/x² - 2 = 5

(x² + 1/x² + 2) - 4 = 5

(x + 1/x)² = 5 + 4

(x + 1/x)² = 9

x + 1/x = √9 = 3

Answer 2

Answer:

$2 - \sqrt{5}$

Step-by-step explanation:

It is given that:   $\frac{x - 1}{x} = \sqrt{5}$

On solving

$\frac{x - 1}{x} = \sqrt{5}\\x-1=x\sqrt{5}\\x - x\sqrt{5} = 1\\x(1-\sqrt{5}) = 1\\x = \frac{1}{1-\sqrt{5}}$

Therefore, we found x

Now lets find $\frac{x + 1}{x}$

$\frac{x + 1}{x} = \frac{\frac{1}{1 - \sqrt{5}} + 1}{\frac{1}{1 - \sqrt{5}}}\\\\=\frac{\frac{1 + 1 - \sqrt{5}}{1 - \sqrt{5}}}{\frac{1}{1 - \sqrt{5}}}\\\\=\frac{\frac{2 - \sqrt{5}}{1 - \sqrt{5}}}{\frac{1}{1 - \sqrt{5}}} = \frac{2 - \sqrt{5}}{1}\\\\= 2 - \sqrt{5}$

Therefore

$\frac{x + 1}{x} = 2 - \sqrt{5}$