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January 19th, 2017, 06:24 AM   #1
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two variable equation

Hi,
Is there any systematic way to solve equations like this
$\displaystyle xy^{2}+y-4y+2=0$
I know the answer is x=y=1
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January 19th, 2017, 06:45 AM   #2
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If you write it as a quadratic, you get

$$y=\frac{3\pm\sqrt{9-8x}}{2x}$$

There are solutions other than the one you mentioned. In fact, for real x and y, there are solutions wherever $9\ge8x$.

x = 1 and y = 2 is another set of solutions in positive integers.
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January 19th, 2017, 10:33 AM   #3
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Quote:
Originally Posted by mhhojati View Post
xy^2+y-4y+2=0
Any reason you did not post your equation this way:
xy^2 - 3y + 2 = 0 ?
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January 20th, 2017, 05:41 AM   #4
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no that equation was part of the solution of another question and I forgot to trim it
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