Question

The sum of the square of a number and one divided by the difference of 1 form the square gives 221 by 220. what is the number

Answer 1

Let the number be x, then

According to question,

$\frac{ {x}^{2} + 1}{1 - {x}^{2} } = \frac{221}{220} \\ \\ 220 {x}^{2} + 220 = 221 - 221 {x}^{2} \\ \\ 441 {x}^{2} = 1 \\ \\ {x}^{2} = \frac{1}{441} \\ \\ x = \frac{1}{21} \: or \: x = - \frac{1}{21}$