The product of two consecutive odd numbers is 143. What are the two numbers?

Answer 1

Let us call the first number x. Then, the second number is x + 2 (i.e. if the first number was 1, the next consecutive odd is 1 + 2 = 3). Thus, we can write that the product of the two numbers is 143 algebraically as x(x + 2) = 143. We can then solve this equation by factoring as follows:

(1) x(x + 2) = 143

(2) x² + 2x = 143

(3) x² + 2x - 143 = 0

(4) (x - 11)(x+13) = 0

(5) x = 11, x = -13

Where we set each expression in parenthesese from step 4 equal to 0. Presumably, we are only interested in positive values of x here. Thus, our two values are 11 and 11 + 2 = 13. We can then verify that 11 and 13 are in fact two consecutive odd numbers, and that their product is 143. I hope this helps!