document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089671>Question 1089671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This problem was labled in my textbook as a nonlinear equation, but I couldn't find a better spot to put it. \r<BR>\n" );
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document.write( " X^2+y^2=3<BR>\n" );
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document.write( " x-y=2\r<BR>\n" );
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document.write( "I'm ending up with x= plus or minus sqrt14/2 my textbook has x as plus or minus 1. <BR>\n" );
document.write( "Could you explain to me where I'm going wrong?\r<BR>\n" );
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document.write( "Thank you!\r<BR>\n" );
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document.write( "p.s. I wasn't quite sure how to notate the fact that the two equations went together so I just did the little brackets between them. I'm not a math person, so if you could be very clear and explicit that would be much appreciated. Thanks again! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704012 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equations are:\r<BR>\n" );
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document.write( "x^2 + y^2 = 3\r<BR>\n" );
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document.write( "x - y = 2\r<BR>\n" );
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document.write( "right off the bat, the book can't be right when it says x is plus or minus 1.\r<BR>\n" );
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document.write( "assuming x is 1, then x^2 + y^2 = 3 becomes 1 + y^2 = 3 which becomes y^2 = 2 which becomes y = plus or minus sqrt(2).\r<BR>\n" );
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document.write( "assuming x is -1, you get the same value for y as y = sqrt(2) becauswe (-1)^2 is also equal to 1.\r<BR>\n" );
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document.write( "however:\r<BR>\n" );
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document.write( "x - y = 2 becomes:\r<BR>\n" );
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document.write( "1 - sqrt(2) = 2 which is false, so x = plus or minus 1 can't be the solution because it doesn't solve both equations simultaneosuly, which i assume is what the problem wants you to solve.\r<BR>\n" );
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document.write( "your solution of x = sqrt(14)/2 doesn't look right either.\r<BR>\n" );
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document.write( "i solved it as follows:\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "x^2 + y^2 = 3<BR>\n" );
document.write( "x - y = 2\r<BR>\n" );
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document.write( "these are 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "solve for y in the second equation to get y = x - 2\r<BR>\n" );
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document.write( "replace y with x-2 in the first equation to get x^2 + (x-2)^2 = 3\r<BR>\n" );
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document.write( "simplify to get x^2 + x^2 - 4x + 4 = 3\r<BR>\n" );
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document.write( "combine like terms to get 2x^2 - 4x + 4 = 3\r<BR>\n" );
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document.write( "subtract 3 from both sides of the equation to get:\r<BR>\n" );
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document.write( "2x^2 - 4x + 1 = 0\r<BR>\n" );
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document.write( "factor this quadratic to get:\r<BR>\n" );
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document.write( "x = 1.7071067811865 or x = 0.29289321881345\r<BR>\n" );
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document.write( "i used an online quaderatic solver at <a  rel=nofollow HREF= \"https://www.mathsisfun.com/quadratic-equation-solver.html\" target = \"-blank\">https://www.mathsisfun.com/quadratic-equation-solver.html</a>\r<BR>\n" );
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document.write( "i also solved it manually using the quadratic formula and got:\r<BR>\n" );
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document.write( "x = 1 + sqrt(2)/2 or x = 1 - sqrt(2)/2\r<BR>\n" );
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document.write( "this resulted in:\r<BR>\n" );
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document.write( "x = 1.707106781 or x = .2928932188\r<BR>\n" );
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document.write( "the results are the same with the exception of the number of decimal digits displayed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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