- #1
fishturtle1
- 394
- 82
Homework Statement
Prove or refute the following conjecture: There are no positive integers x and y such that ##x^2 - 3xy + 2y^2 = 10##
Homework Equations
##10 = 5*2##
##10 = 10*1##
The Attempt at a Solution
I graphed it using a graphing calculator, so I know this is true.
Proof: This will be a proof by contradiction. Suppose ##x## and ##y## are positive integers and ##x^2 - 3xy + 2y^2 = 10##. By factoring, we have ##(x-2y)(x-y) = 10##.
im not sure how to get further..
Like I did in the previous problem, I tried to set ##x-2y = 10##, then ##x-y = 10 + y## but I don't think I can get a contradiction on this path