Question

If x+1/x = 12, find the value of x-1/x and x^2+1/x^2.​

Answer 1

Step-by-step explanation:

$x + \frac{1}{x} = 12 \\ \\ squaring \: on \: both \: sides \: \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 144 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 142 \\ \\ ( {x - \frac{1}{x} })^{2} + 2 = 142 \\ {(x - \frac{1}{x} })^{2} = 140 \\ x - \frac{1}{x} = \sqrt{140} = 2 \sqrt{35} \\ \\ hope \: it \: will \: help \: you$