find 3 consecutive odd integers such that the product of the first and the second exceeds the third by 8.

Answer 1

3, 5, and 7
?

Answer 2

Let x be the middle odd integer. Then the smaller odd integer is x-2, and the bigger is x+2

The problem requires that
x(x-2)-(x+2) = 8

or

x² - 3x -10 = 0

Solution of the quadratic equation gives
x= -2 or x = 5
Since -2 is not an odd integer, it will be discarded.

Thus the three consecutive odd integers are
3,5,7

Check:
3*5-7=8 OK

Answer 3

Find three consecutive odd integers such that the product of the first and the second exceeds the third by 8