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Question 805454: the question is " solve all positive integers (x,y) that satisfy: x^2-4xy+3y^2=17"
i factored it down to (x-y)(x-3y)-17=0. and now i don't know what to do. Could you possibly walk me through the rest of the problem?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! the question is " solve all positive integers (x,y) that satisfy:
x^2-4xy+3y^2=17
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(x-y)(x-3y) = 17
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Since 17 is a prime number,
x-y = 1 and x-3y = 17
Then y+1-3y = 17
-2y = 16
y = -8
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And x = y+1 = -7
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OR
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x-y = 17 and x-3y = 1
y+17 -3y = 1
-2y = -16
y = 8
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And x = y+17 = 25
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Since you are asked for Positive solutions,
x = 25 and y = 8
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Cheers,
Stan H.
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