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March 5th, 2013, 10:59 PM  #1 
Newbie Joined: Mar 2013 Posts: 20 Thanks: 0  Please help, I cannot figure this out, very short question.
A folium of Descartes is given by x^3 + y^3 = 18xy. a) Find the integer value of y for the point on the curve when x = 8. Please answer in steps so that I may know how to do this in the future. Thank you so much. 
March 5th, 2013, 11:29 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: Please help, I cannot figure this out, very short questi
Let and write the resulting cubic in . Next apply the rational roots theorem to find the integral zero. What do you find?

March 5th, 2013, 11:41 PM  #3  
Newbie Joined: Mar 2013 Posts: 20 Thanks: 0  Re: Please help, I cannot figure this out, very short questi Quote:
I tried many ways to go beyond this formula and finding the possible roots for these numbers but this is where I get stuck I cannot find the two roots which would satisfy all the conditions. Thanks.  
March 5th, 2013, 11:47 PM  #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: Please Help, I cannot figure this out, very short questi
There are 3 roots, but only 1 is an integer. The rational roots theorem tells us it will come from the list: So, let Now, try values from the above list, until you find a value for such that . 
March 5th, 2013, 11:49 PM  #5 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Please help, I cannot figure this out, very short questi
@MarkFL : I doubt if the asker knows Rational root test. The best way is to iterate and you'll find an integral root. Then use synthetic division to find the quadratic and use quadratic formula to see if there are any other roots. 
March 5th, 2013, 11:58 PM  #6  
Newbie Joined: Mar 2013 Posts: 20 Thanks: 0  Re: Please help, I cannot figure this out, very short questi Quote:
I get it now, thank you Mark  
March 6th, 2013, 05:56 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: Please help, I cannot figure this out, very short questi
Substituting x = 8 then dividing y³  144y + 512 by y  4 gives y²  4y  128, which has no integer roots.

March 6th, 2013, 07:49 AM  #8  
Global Moderator Joined: Dec 2006 Posts: 20,927 Thanks: 2205  Quote:
 

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