Question

x-(1)/(x) and x^(2)-(1)/(x^(2)) if x+(1)/(x)=sqrt(5)​

Answer 1

Answer:

Given,

$x + \frac{1}{x} = \sqrt{5} \\ then \: \: {(x - \frac{1}{x} )}^{2} = {(x + \frac{1}{x}) }^{2} - 4 \times x \times \frac{1}{x} \\ {(x - \frac{1}{x} )}^{2} = { \sqrt{5} }^{2} - 4 = 1 \\ x - \frac{1}{x} = 1$

and

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

Ans.