Question

Two sets of three consecutive integers have a property that the product of the larger two is one less than seven times the smallest.set up and solve an equation that can be used to find both sets of integers

Answer 1

(x + 1)(x + 2) = 7x - 1

{1, 2, 3} and {3, 4, 5}

Explanation:

Let the three consecutive integers be x, x + 1, and x + 2.

(x + 1)(x + 2) = 7x - 1

x² + 3x + 2 - 7x + 1 = 0

x² - 4x + 3 = 0

(x - 3)(x - 1) = 0

x - 3 = 0 or x - 1 = 0

x = 3 or x = 1

For x = 1,

x = 1, x + 1 = 2, x + 2 = 3

For x = 3,

x = 3, x + 1 = 4, x + 2 = 5

Answer: {1, 2, 3} and {3, 4, 5}