Find 3 consecutive integers such as that the product of the 1st and 2nd integers are equal to 2 more than 6 times the 3rd

Question

Need help please!!!!!! I really need help

Answer 1

Examples of consecutive integers 3, 4, 5 or 7, 8 ,9 or -4, -5, -6 etc. Note that each number is one more than the previous number. Since our consecutive numbers are unknown, we call them x, x+1, and x+2. We want product of the 1st and 2nd integers ( (x(x+1) ) to be equal to 2 more than 6 times the 3rd =( 6(x+2) + 2 ):

x(x+1) = 6(x+2) + 2

x² + x = 6x + 12 + 2

x² + x = 6x + 14

x² - 5x - 14 = 0

Solve for x by factoring. You will get two values for x, so there are two sets of consecutive integers that meet the criteria.