January 19th, 2017, 06:24 AM  #1 
Member Joined: Jan 2012 Posts: 57 Thanks: 0  two variable equation
Hi, Is there any systematic way to solve equations like this $\displaystyle xy^{2}+y4y+2=0$ I know the answer is x=y=1 thanks 
January 19th, 2017, 06:45 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,743 Thanks: 1001 Math Focus: Elementary mathematics and beyond 
If you write it as a quadratic, you get $$y=\frac{3\pm\sqrt{98x}}{2x}$$ 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. 
January 19th, 2017, 10:33 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 11,672 Thanks: 741  
January 20th, 2017, 05:41 AM  #4 
Member Joined: Jan 2012 Posts: 57 Thanks: 0 
no that equation was part of the solution of another question and I forgot to trim it


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