Question

if x+1/x=6, find (i) x-1/x (ii) x2-1/x2​

Answer 1

$x + \frac{1}{x} = 6...(1) \\ ( {x + \frac{1}{x} })^{2} = 36 \\ ( {x - \frac{1}{x} })^{2} + 4 = 36 \\ ( {x - \frac{1}{x} })^{2} = 32 \\ x - \frac{1}{x} = 4 \sqrt{2} ...(2) \\ finding \: \: \: {x}^{2} - \frac{1}{ {x}^{2} } = (x + \frac{1}{x} )(x - \frac{1}{x} ) \\ = 6 \times 4 \sqrt{2} \\ = 24 \sqrt{2}$