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 November 9th, 2018, 10:38 PM #1 Senior Member   Joined: Jul 2011 Posts: 405 Thanks: 16 Number of rational points The number of rational points on the circle with center $(\sqrt{2},-\sqrt{2})$ and which passes through $(1,-1)$ is November 9th, 2018, 11:47 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,968 Thanks: 2217 At a guess, 1. Thanks from topsquark November 10th, 2018, 05:10 PM #3 Global Moderator   Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond For $x=1$ and $y=-1$, $\displaystyle (x-\sqrt2)^2+(y+\sqrt2)^2=6-4\sqrt2$ Generally, if $x$ and $y$ are rational, $\displaystyle x^2-2\sqrt2x+2+y^2+2\sqrt2y+2=6-4\sqrt2$ $\displaystyle x^2+y^2+2\sqrt2(y-x)=2-4\sqrt2$ $\displaystyle \implies x^2+y^2=2$ $\displaystyle \implies x-y=2$ $\displaystyle (y+2)^2+y^2=2$ $\displaystyle 2y^2+4y+2=0\implies y=\frac{-4\pm0}{4}$ $\displaystyle x^2+(x-2)^2=2$ $\displaystyle 2x^2-4x+2=0\implies x=\frac{4\pm0}{4}$ Looks like skipjack's guess is correct. Thanks from topsquark Last edited by greg1313; November 10th, 2018 at 05:44 PM. Tags number, points, rational Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Roli Algebra 14 June 10th, 2014 01:40 AM Tzad Calculus 8 November 7th, 2013 07:55 PM tva_vlad Algebra 1 October 7th, 2013 01:38 AM Rejjy Algebra 2 December 1st, 2012 02:41 AM guru123 Algebra 18 June 22nd, 2012 01:38 PM

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