document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129186>Question 1129186</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use any method to solve the nonlinear system. (Order your answers from smallest to largest x, then from smallest to largest y. If there is no solution, enter NO SOLUTION.)\r<BR>\n" );
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document.write( "x^2  + y^2= 6<BR>\n" );
document.write( "xy= 1\r<BR>\n" );
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document.write( "Can someone help, I use the method of and  my final answers, which keeps being tagged incorrect, have been: <BR>\n" );
document.write( "x:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -1, y:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+2+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > +1<BR>\n" );
document.write( "x: - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > +1, y: -  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+2+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > -1<BR>\n" );
document.write( "x:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > +1,  y:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+2+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-1<BR>\n" );
document.write( "x: -  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > -1, y: -  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+2+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > +1\r<BR>\n" );
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document.write( "Am I just incorrectly ordering them from smallest to least or are the entire answers wrong? <BR>\n" );
document.write( "Here is some of my work: <BR>\n" );
document.write( "For x^2 + y^2= 6, substitute x with 1/y.<BR>\n" );
document.write( "(1/y)^2 +y^2= 6; \r<BR>\n" );
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document.write( "For xy=1, substitute y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > +1<BR>\n" );
document.write( "x(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > +1  )=1 <BR>\n" );
document.write( "x= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > -1\r<BR>\n" );
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document.write( "For xy=1, substitute y with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > -1<BR>\n" );
document.write( "x(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > -1  )=1 <BR>\n" );
document.write( "x= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > +1\r<BR>\n" );
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document.write( "For xy=1, substitute y with -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > +1<BR>\n" );
document.write( "x(-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > +1  )=1 <BR>\n" );
document.write( "x= -<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > -1\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #745739 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=745739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2=+6 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=+1 ALIGN=MIDDLE  ALT=\"xy=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ........eq.2<BR>\n" );
document.write( "-----------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=+1 ALIGN=MIDDLE  ALT=\"xy=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ........eq.2=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2Fy ALIGN=MIDDLE  ALT=\"x=1%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "substitute in eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fy%29%5E2+%2B+y%5E2=+6 ALIGN=MIDDLE  ALT=\"%281%2Fy%29%5E2+%2B+y%5E2=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >........eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fy%5E2+%2B+y%5E2=+6 ALIGN=MIDDLE  ALT=\"1%2Fy%5E2+%2B+y%5E2=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >...multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B+y%5E4=+6y%5E2 ALIGN=MIDDLE  ALT=\"1+%2B+y%5E4=+6y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E4-+6y%5E2%2B1=0 ALIGN=MIDDLE  ALT=\"+y%5E4-+6y%5E2%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2+-+2+y+-+1%29+%28y%5E2+%2B+2+y+-+1%29=0 ALIGN=MIDDLE  ALT=\"%28y%5E2+-+2+y+-+1%29+%28y%5E2+%2B+2+y+-+1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions: there will be four   \r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2+-+2+y+-+1%29+=0 ALIGN=MIDDLE  ALT=\"%28y%5E2+-+2+y+-+1%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"y+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282+%2B-+sqrt%28+4%2B4%29%29%2F2+ ALIGN=MIDDLE  ALT=\"y+=+%282+%2B-+sqrt%28+4%2B4%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282+%2B-+sqrt%28+2%2A4%29%29%2F2+ ALIGN=MIDDLE  ALT=\"y+=+%282+%2B-+sqrt%28+2%2A4%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282+%2B-+2sqrt%28+2%29%29%2F2+ ALIGN=MIDDLE  ALT=\"y+=+%282+%2B-+2sqrt%28+2%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281+%2B-+sqrt%28+2%29%29+ ALIGN=MIDDLE  ALT=\"y+=+%281+%2B-+sqrt%28+2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y+%5B1%5D=+1+%2B+sqrt%28+2%29%29+ ALIGN=MIDDLE  ALT=\"highlight%28y+%5B1%5D=+1+%2B+sqrt%28+2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y%5B2%5D+=+1+-+sqrt%28+2%29%29+%29 ALIGN=MIDDLE  ALT=\"highlight%28y%5B2%5D+=+1+-+sqrt%28+2%29%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28y%5E2+%2B+2+y+-+1%29=0 ALIGN=MIDDLE  ALT=\"+%28y%5E2+%2B+2+y+-+1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"y+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2+%2B-+sqrt%28+4%2B4+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"y+=+%28-2+%2B-+sqrt%28+4%2B4+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-2+%2B-+2sqrt%282+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"y+=+%28-2+%2B-+2sqrt%282+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28-1+%2B-+sqrt%282+%29%29+ ALIGN=MIDDLE  ALT=\"y+=+%28-1+%2B-+sqrt%282+%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y%5B3%5D+=+-1+%2B+sqrt%282+%29+%29 ALIGN=MIDDLE  ALT=\"highlight%28y%5B3%5D+=+-1+%2B+sqrt%282+%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y%5B4%5D+=+-1+-+sqrt%282+%29+%29 ALIGN=MIDDLE  ALT=\"highlight%28y%5B4%5D+=+-1+-+sqrt%282+%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > using all 4 solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%5B1%5D=+1+%2B+sqrt%28+2%29+ ALIGN=MIDDLE  ALT=\"y+%5B1%5D=+1+%2B+sqrt%28+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2Fy ALIGN=MIDDLE  ALT=\"x=1%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+1%2F%281+%2B+sqrt%28+2%29%29=+%281+-+sqrt%28+2%29%29%2F%28%281+%2B+sqrt%28+2%29%29%281+-+sqrt%28+2%29%29%29=%281+-+sqrt%28+2%29%29%2F%281%5E2+-+%28sqrt%28+2%29%29%5E2%29=%281+-+sqrt%28+2%29%29%2F%281+-+2%29=%281+-+sqrt%28+2%29%29%2F-1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B1%5D=sqrt%282%29+-+1%29+%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5B1%5D=sqrt%282%29+-+1%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%5B2%5D=+1+-+sqrt%28+2%29+ ALIGN=MIDDLE  ALT=\"y+%5B2%5D=+1+-+sqrt%28+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+1%2F%281+-+sqrt%28+2%29%29=+%281+%2B+sqrt%28+2%29%29%2F%28%281+%2B+sqrt%28+2%29%29%281+-+sqrt%28+2%29%29%29=%281+%2B+sqrt%28+2%29%29%2F%281%5E2+-+%28sqrt%28+2%29%29%5E2%29=%281+%2Bsqrt%28+2%29%29%2F%281+-+2%29=%281%2Bsqrt%28+2%29%29%2F-1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B2%5D=+-+1-sqrt%282%29%29+ ALIGN=MIDDLE  ALT=\"highlight%28x%5B2%5D=+-+1-sqrt%282%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B3%5D+=+-1+%2B+sqrt%282+%29=+sqrt%282+%29-1 ALIGN=MIDDLE  ALT=\"y%5B3%5D+=+-1+%2B+sqrt%282+%29=+sqrt%282+%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+1%2F%28sqrt%28+2%29-1%29=%28sqrt%28+2%29%2B1%29%2F%28%28sqrt%28+2%29%29%5E2-1%5E2%29=%28sqrt%28+2%29%2B1%29%2F%282-1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B3%5D=sqrt%28+2%29%2B1%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5B3%5D=sqrt%28+2%29%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B4%5D+=+-1+-+sqrt%282+%29+ ALIGN=MIDDLE  ALT=\"y%5B4%5D+=+-1+-+sqrt%282+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+1%2F%28-1+-+sqrt%282+%29%29=%28-1+%2B+sqrt%282+%29%29%2F%28%28%28-1%29%5E2+-+%28sqrt%282+%29%29%5E2%29%29=%28-1+%2B+sqrt%282+%29%29%2F%281-2%29=%28-1+%2B+sqrt%282+%29%29%2F-1=-%28-1+%2B+sqrt%282+%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x%5B4%5D=1-sqrt%282+%29%29 ALIGN=MIDDLE  ALT=\"highlight%28x%5B4%5D=1-sqrt%282+%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );