Question

The product of two consecutive odd natural numbers is 1 less than 6 times their sum. Find the numbers.

Answer 1

11 ; 13

Explanation:

Let the numbers be :

x and x + 2

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

x² + 2x = 6(2x + 2) - 1

x² + 2x = 12x + 12 - 1

x² + 2x = 12x + 11

x² + 2x - 12x - 11 = 0

x² - 10x + 11 = 0

x² - 11x + x + 11 = 0

x(x - 11) + 1(x - 11) = 0

(x - 11) = 0 or (x + 1) = 0

x = 11 or x = - 1

X cannot be negative

x = 11

x + 2 = 11 +2 = 13