find three consecutive odd integers such that the product of the first and third is 71 more than 10 times the second

13, 15, 17

Step-by-step explanation:

x (x + 4) = 10 (x + 2) + 71

x2 + 4x = 10x + 20 + 71

x2 - 6x - 91 = 0

(x + 7) (x - 13) = 0

x + 7 = 0

x = - 7

-7, - 5, - 3

x - 13 = 0

x = 13

13, 15, 17