Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: suppose I have an equation x^2+x+y^2+3*y=5*y^2+3*y+3*x*y+5 and Date: Thu, 12 Aug 2010 17:35:05 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 19 Message-ID: <i41bc9$ioh$1@fred.mathworks.com> References: <i40rce$qur$1@fred.mathworks.com> <1780645233.99952.1281623886497.JavaMail.root@gallium.mathforum.org> <i413a4$682$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: webapp-05-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1281634505 19217 172.30.248.35 (12 Aug 2010 17:35:05 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Thu, 12 Aug 2010 17:35:05 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:661509 "Kittithad Wangveerathananon" <kittithad@startfromyou.com> wrote in message <i413a4$682$1@fred.mathworks.com>... > all points of the form > (1.5y-0.5 + 0.5*sqrt(25y^2-6y+21),y) or > (1.5y-0.5 - 0.5*sqrt(25y^2-6y+21),y) > > If I sub the value of y, freely, i might get 1.5y-0.5 + 0.5*sqrt(25y^2-6y+21) as a complex number right? > > I try this way before too and get the complex number. > ....... - - - - - - - - - - No, that isn't correct! Torsten has given you a valid solution. For all real y numbers Torsten's quantity inside the square root is always a positive quantity and can never give you a complex result for x. Write it like this: 25y^2-6y+21 = (5*y-3/5)^2+516/25 and you can see that it can never be less that 516/25, no matter what x is. The locus of your equation is a hyperbola in which the two branches lie to the left and the right. There are some x's in between for which no real y exists, but for every possible real y there are two distinct x's which satisfy the equation. Roger Stafford