Question

x-1/x &. x^2-1/x^2
if x+1/x = √5​

Answer 1

Step-by-step explanation:

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

${x}^{2} + \frac{1}{ {x}^{2} } + 2 = 5$

${x}^{2} + \frac{1}{ {x}^{2} } = 3$

$let \: x - \frac{1}{x} = a$

${x}^{2} + \frac{1}{ {x}^{2} } - 2 = {a}^{2}$

$3 - 2 = {a}^{2}$

${a}^{2} = 1$

$a = 1 = x - \frac{1}{x}$

${x}^{2} - \frac{1}{ {x}^{2} } = (x + \frac{1}{x} )(x - \frac{1}{x} )$

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

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

Therefore, it is your answer.

I hope it helps you. If you have any doubts, then don't hesitate to ask.