Question

the difference between 2 integers is 4. their product is 221. Find the numbers. (ans: 13, 17 or -13, -17)

Answer 1

let the number x and y
$x - y = 4 \\ xy = 221 \\ x = \frac{221}{y} \\ \frac{221}{y} - y = 4 \\ 221 - {y}^{2} = 4y \\ - {y}^{2} - 4y + 221 = 0 \\ {y}^{2} + 4y - 221 = 0 \\ {y}^{2} - 17y + 13y - 221 = 0 \\ y(y - 17) + 13(y - 17) = 0 \\ (y + 13)(y - 17) = 0 \\ y = - 13 \\ y = 17$
put these values of y into any of the equation.

xy= 221
$x = \frac{221}{ - 13} = - 17 \\ x = \frac{221}{17 } = 13$

Answer 2

Answer:

y= -13 and y= 17

Step-by-step explanation:

let the number be x and y