Question

One integer is 7 more than another. Their product is 98. Find the integers,

Answer 1

- 14, - 7 or 7, 14

Explanation:

Let the the two integers be x and (x + 7)

`\therefore \: x(x + 7) = 98 \\ {x}^(2) + 7x - 98 = 0 \\ {x}^(2) + 14x - 7x - 98 = 0 \\ x(x + 14) - 7(x + 14) = 0 \\ (x + 14)(x - 7) = 0 \\ (x + 14) = 0 \: or \: (x - 7) = 0 \\ x = - 14 \: or \: x = 7 \\ \\ when \: x = - 14 \\ x + 7 = - 14 + 7 = - 7 \\ \\ when \: x = 7 \\ x + 7 = 7 + 7 = 14 \\`

Hence the required integers are - 14, - 7 or 7, 14