Question

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46. Find the integers.

(a) 1, 2, 3
(b) 2, 3, 4
(c) 3, 4, 5
(d) 4, 5, 6

Answer 1

To solve the problem, let x, x+1, and x+2 represent the three consecutive integers. Using the given equation and the quadratic formula, we find that the integers are 4, 5, and 6.

Step-by-step explanation:

To solve the problem, we need to represent the three consecutive integers as x, x+1, and x+2. According to the given information, we have the equation x^2 + (x+1)(x+2) = 46. Expanding and simplifying the equation gives x^2 + 3x + 2 = 46. Rearranging the equation to the form x^2 + 3x - 44 = 0, we can solve for x using the quadratic formula. The solutions are x = 4 and x = -11. Since we are looking for positive integers, the three consecutive integers are 4, 5, and 6 (option d).