The product of two consecutive positive integers is greater than their sum by 209. find these numbers.

The two consecutive integers are 15 and 14 respectively

let

x = first positive integer

x + 1 = second positive integer

x(x + 1) > x + (x + 1) + 209

x² + x > x + x + 1 + 209

x² + x > 2x + 210

x² + x - 2x > 210

x² - x > 210

x² - x - 210 > 0

solve be quadratically using factorization method

x² - 15x + 14x - 210 > 0

x(x - 15) + 14(x - 15) > 0

(x - 15) (x + 14) > 0

x -15 > 0. x + 14 > 0

x > 15. x > - 14

Therefore, the two consecutive integers are 15 and 14 respectively

Learn more about consecutive numbers:

link

15, 16

Step-by-step explanation:

so, x(x+1)=x+x+1+209.solve this and you get x^2+x=2x=210, x^2-x-210=0, and when you solve this quadratic function, you get x=15, and the other with 16. to check see if 240 is 209 greater than 31, which is so there you have it. Hope you have a happy thanksgiving!