no +ve integer x & y such that, x^2 - 3xy + 2y^2 = 10

Question

agent0smith · Answer

not sure what the exact question is, but it seems like you need to factor it:$$\large (x -2y)(x-y) = 10$$now each of the brackets must be factors of 10 (since i'm assuming they're only allowing integers)

agent0smith · Answer

eg one bracket must be equal to 1, the other must be equal to 10
or one is equal to 2, and the other 5

those are the only factors of 10. You can use them to make simultaneous equations.

anonymous · Answer

Prove or disprove there are no positive integers x and y such that; $$x^2 -3xy+2y^2=10$$

anonymous · Answer

Not sure how to do it through induction.

agent0smith · Answer

x-2y = 10 and x-y = 1

or

x-2y = 1 and x-y = 10

or

x-2y = 5 and x-y = 2

or

x-2y = 2 and x-y = 5


with those you can prove it and it won't take long.

agent0smith · Answer

If there are any positive integers, those will find them.

anonymous · Answer

cheers mate

agent0smith · Answer

oh, actually, you'd also need to check for cases when both factors are -ve...
ie -1 and -10, and -2 and -5