SOLUTION: Find 3 odd consecutive intergers such that the product of the first and third minus the middle intergers is 338.

Find 3 odd consecutive integers such that the product of the first and third minus the middle integer is 338.
Ans:
Let the 3 odd integers be n-2,n and n+2
Product of 1st and 3rd = 
Subtracting middle integer

Or

This is a simple quadratic equation which can be solved by factorizing.


So possible solutions for n are  or 

Correspondingly, the 3 numbers are (-20,-18,-16) or (17,19,21)

Since is is not mentioned that the integers are positive, both solutions are valid.

Check: 

Both are correct!

:)