Find two consecutive odd integers such that their product is 31 more than 2 times their sum

Answer 1

The consecutive odd integers are 2k - 1 and 2k + 1

The product of the integers is 4k² - 1 and the sum is 4k.

2x the sum plus 31 is 8k + 31 and this equals the product

hence

8k + 31 = 4k² - 1

This factors and both roots give acceptable answers.

I will leave the factoring to you...and if you can't factor, use the quadratic formula.