Quandaries and Queries
  

 

I am having trouble solving the following problem.
If x and y are integers, when will x squared+xy+(y-x) be even?
I don't really know where to begin or how to even go about solving this problem. Please Help! Thanks
-Lana
 

 

Hi Lana,

I would do this with four cases.

  1. Both x and y are even.

  2. Both x and y are odd.

  3. x is even and y is odd.

  4. y is even and x is odd.

Case 1.

If both x and y are even then x2 is even, xy is even and y-x is even so x2 + xy + (y-x) is even.

Case 2.

If both x and y are odd then x2 is odd, xy is odd and y-x is even so x2 + xy + (y-x) is even.

I have left the other two cases for you.

Penny