December 17th, 2012, 11:29 PM  #1 
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Find x and y. I know answer is (3;1) but I am looking for another root(s). I got this 
December 17th, 2012, 11:45 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Find x and y.
I would use the first equation, and substitute into the second, to get the quartic in : and then use a numeric root finding technique to approximate the other 3 irrational roots: 
December 18th, 2012, 04:12 AM  #3 
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Find x and y.
Only one of these irrational roots may be correct. I analyzed my incomplete solution . a is near to 4

December 18th, 2012, 04:17 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Find x and y.
They are all correct. You have made an error with your incomplete solution.

December 18th, 2012, 04:51 AM  #5  
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Find x and y. Quote:
 
December 18th, 2012, 05:09 AM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Find x and y.
I have already shown the numerically approximated roots. I'm not going to manually grind out the 3 irrational roots using the NewtonRaphson method, since that is a technique from differential calculus. If you feel incomplete with these roots as given, then try the quartic formula.

December 18th, 2012, 05:33 AM  #7  
Senior Member Joined: Dec 2012 Posts: 148 Thanks: 0  Re: Find x and y. Quote:
 

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