document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=944234>Question 944234</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two positive numbers that differ by eight and whose reciprocals sum is 1/6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575702 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=575702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "let two positive numbers be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <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 they differ by eight, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=8 ALIGN=MIDDLE  ALT=\"x-y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B8 ALIGN=MIDDLE  ALT=\"x=y%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >......eq.1\r<BR>\n" );
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document.write( " and if their reciprocals sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   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=1%2Fx%2B1%2Fy=1%2F6 ALIGN=MIDDLE  ALT=\"1%2Fx%2B1%2Fy=1%2F6\"   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%2Fxy%2Bx%2Fxy=1%2F6 ALIGN=MIDDLE  ALT=\"y%2Fxy%2Bx%2Fxy=1%2F6\"   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=%28y%2Bx%29%2Fxy=1%2F6 ALIGN=MIDDLE  ALT=\"%28y%2Bx%29%2Fxy=1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28y%2Bx%29=1%2Axy ALIGN=MIDDLE  ALT=\"6%28y%2Bx%29=1%2Axy\"   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=6y%2B6x=xy ALIGN=MIDDLE  ALT=\"6y%2B6x=xy\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....eq.2 ....substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from eq.1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6y%2B6%28y%2B8%29=%28y%2B8%29y ALIGN=MIDDLE  ALT=\"6y%2B6%28y%2B8%29=%28y%2B8%29y\"   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=6y%2B6y%2B48=y%5E2%2B8y ALIGN=MIDDLE  ALT=\"6y%2B6y%2B48=y%5E2%2B8y\"   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=12y%2B48=y%5E2%2B8y ALIGN=MIDDLE  ALT=\"12y%2B48=y%5E2%2B8y\"   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=0=y%5E2%2B8y-12y-48 ALIGN=MIDDLE  ALT=\"0=y%5E2%2B8y-12y-48\"   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%5E2-4y-48=0 ALIGN=MIDDLE  ALT=\"y%5E2-4y-48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....use quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%2B2sqrt%2813%29=9.211102550927979 ALIGN=MIDDLE  ALT=\"y+=+2%2B2sqrt%2813%29=9.211102550927979\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "y = 2-2 sqrt(13)=-5.2 we need positive number only\r<BR>\n" );
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document.write( "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;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B8 ALIGN=MIDDLE  ALT=\"x=y%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=9.2%2B8=17.211102550927979 ALIGN=MIDDLE  ALT=\"x=9.2%2B8=17.211102550927979\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "check the sum of reciprocals:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%2B1%2Fy=1%2F6 ALIGN=MIDDLE  ALT=\"1%2Fx%2B1%2Fy=1%2F6\"   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%2F17.211102550927979%2B1%2F9.211102550927979=0.1666666666666667 ALIGN=MIDDLE  ALT=\"1%2F17.211102550927979%2B1%2F9.211102550927979=0.1666666666666667\"   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=0.0581020301890005%2B0.1085646364776662=0.1666666666666667 ALIGN=MIDDLE  ALT=\"0.0581020301890005%2B0.1085646364776662=0.1666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.1666666666666667=0.1666666666666667 ALIGN=MIDDLE  ALT=\"0.1666666666666667=0.1666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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