Question

The difference between a number and its inverse is 80 by 9 find these numbers

Answer 1

$let \: one \: number \: be \: x \\ atq. \\ x - \frac{1}{x} = \frac{80}{9} \\ or \: 9x {}^{2} - 9 = 80x \\ or \: 9x {}^{2} - 80 x - 9 = 0 \\ or \: (x - 9)(9x + 1) = 0 \\ or \: x = 9 \: or \: \frac{ - 1}{9}$

so the pair of numbers will be (9, 1/9) and (-9, -1/9)