Question

if x - 1/x = -1, find the value of x + 1/x​

Answer 1

Step-by-step explanation:

the required answer is√5

Answer 2

$\purple{\mathbb{ANSWER:-}}$

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

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

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

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

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

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

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

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

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

$\sf ∴ x + \frac{1}{x} = ± \sqrt{5}$