Question

Consider two consecutive positive integers such that the square of the second integer added to 3 times the first is equal to 105

Answer 1

8 and 9

Explanation:

If x is the smaller integer, and x + 1 is the larger integer, then:

(x + 1)² + 3x = 105

x² + 2x + 1 + 3x = 105

x² + 5x − 104 = 0

(x + 13) (x − 8) = 0

x = -13 or 8

Since x is positive, x = 8. So the two integers are 8 and 9.