document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42036>Question 42036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two positive real numbers that differ by 1 and have a product of 1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27187 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let 2 numbers be x and y\r<BR>\n" );
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document.write( "We are told:<BR>\n" );
document.write( "x-y=1\r<BR>\n" );
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document.write( "and <BR>\n" );
document.write( "xy=1\r<BR>\n" );
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document.write( "Right then:<BR>\n" );
document.write( "xy=1<BR>\n" );
document.write( "means that x=1/y\r<BR>\n" );
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document.write( "so we then get from x-y=1 that<BR>\n" );
document.write( "(1/y)-y=1<BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1-y%5E2+=+y+ ALIGN=MIDDLE  ALT=\"+1-y%5E2+=+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+-+y%5E2+-+y+=+0+ ALIGN=MIDDLE  ALT=\"+1+-+y%5E2+-+y+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and re-arranging, gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2+%2B+y+-+1+=+0+ ALIGN=MIDDLE  ALT=\"+y%5E2+%2B+y+-+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Not easy to factorise, so use the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%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-%281%29+%2B-+sqrt%28%281%29%5E2+-+4%281%29%28-1%29%29%29%2F%282%281%29%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-%281%29+%2B-+sqrt%28%281%29%5E2+-+4%281%29%28-1%29%29%29%2F%282%281%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=+y+=+%28-1+%2B-+sqrt%281%2B4%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-1+%2B-+sqrt%281%2B4%29%29%2F%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=+y+=+%28-1+%2B-+sqrt%285%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-1+%2B-+sqrt%285%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember, we want positive answers, so of the 2 answers quoted above, only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-1+%2B+sqrt%285%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+y+=+%28-1+%2B+sqrt%285%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is acceptable.\r<BR>\n" );
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document.write( "Now, if x-y=1 then x = 1+y. So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B+sqrt%285%29%29%2F%282%29+%2B+1+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B+sqrt%285%29%29%2F%282%29+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B+sqrt%285%29%29%2F%282%29+%2B+2%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B+sqrt%285%29%29%2F%282%29+%2B+2%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-1+%2B+2+%2B+sqrt%285%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-1+%2B+2+%2B+sqrt%285%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%281+%2B+sqrt%285%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+x+=+%281+%2B+sqrt%285%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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