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 December 17th, 2012, 11:29 PM #1 Senior Member   Joined: Dec 2012 Posts: 148 Thanks: 0 Find x and y. $x^2 +y= 10 \\ x + y^2 = 4$ I know answer is (3;1) but I am looking for another root(s). I got this $\fbox{ x= \frac{ 6 + a + a^2 }{2a} \\ y = \frac{ 6 + a - a^2 }{2a} }$
 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 $x$: $x+$$10-x^2$$^2=4$ $x^4-20x^2+x+96=0$ $(x-3)$$x^3+3x^2-11x-32$$=0$ and then use a numeric root finding technique to approximate the other 3 irrational roots: $x\approx-3.5709287407546415449,\,-2.7216512006427414436,\,3.2925799413973829885$
 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 $4 \ll a \ll 5$ . 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
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Re: Find x and y.

Quote:
 Originally Posted by MarkFL They are all correct. You have made an error with your incomplete solution.
Can you show your solution. Just capture with webcam and upload.

 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 Newton-Raphson 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
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Re: Find x and y.

Quote:
 Originally Posted by MarkFL I have already shown the numerically approximated roots. I'm not going to manually grind out the 3 irrational roots using the Newton-Raphson method, since that is a technique from differential calculus. If you feel incomplete with these roots as given, then try the quartic formula.
OK, I will try, after watching american horror story:asylum

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