Question

The product of two consecutive positive integers is 167 more than the next integer. What is the largest of the three integers?

Answer 1

Explanation:

Let the three consecutive positive integers be x, (x + 1) & (x + 2)

Therefore, according to the given condition:

`x(x + 1) = (x + 2) + 167 \\ \\ \therefore \: {x}^(2) + x = x + 169 \\ \\ \therefore \: {x}^(2) + x - x = 169\\ \\ \therefore \: {x}^(2) = 169 \\ \\ \therefore \: {x} = \pm √(169) \\ \\ \therefore \: {x} = \pm 13 \\ \\ \because \: x \: is \: positive \: \\ \\ \therefore \: x \: \\eq \: - 13 \\ \\ \therefore \: x \: = \: 13 \\ \\\therefore \: x + 2\: = \: 13 + 2 = 15`

Thus, the largest integer is 15.