- #1

- 334

- 44

## 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