Question

The product of two consecutive integers is 98 more than the next integer. What is the largest of the three integers?

Answer 1

let the numbers be x, x+1, x+2

$x(x + 1) = x + 2 + 98 \\ {x}^{2} + x = x + 100 \\ {x}^{2} = 100 \\ x = \sqrt{100} \\ x = 10$

therefore the numbers are

10, 11, 12

the largest integer is 12