document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147791>Question 147791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two positive numbers have a difference of 2 and their reciprocals have a sum of 20/21. What are the numbers?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108175 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x= the larger number; 1/x is the reciprocal<BR>\n" );
document.write( "Then x-2=the smaller number;  1/(x-2) is the reciprocal\r<BR>\n" );
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document.write( "Now we are told that:\r<BR>\n" );
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document.write( "(1/x)+1/(x-2)=20/21  multiply each term by 21x(x-2)<BR>\n" );
document.write( "21(x-2)+21x=20x(x-2)  get rid of parens\r<BR>\n" );
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document.write( "21x-42+21x=20x^2-40x  subtract 20x^2 from and add 40x to both sides<BR>\n" );
document.write( "21x-42+21x-20x^2+40x=20x^2-20x^2-40x+40x  collect like terms\r<BR>\n" );
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document.write( "82x-20x^2-42=0  multiply each term by -1 and rearrange\r<BR>\n" );
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document.write( "20x^2-82x+42=0  divide each term by 2<BR>\n" );
document.write( "10x^2-41x+21=0--------------quadratic in standard form; solve using the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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+=+%2841+%2B-+sqrt%28+%28-41%29%5E2-4%2A10%2A21%29%29%2F%2820%29+ ALIGN=MIDDLE  ALT=\"x+=+%2841+%2B-+sqrt%28+%28-41%29%5E2-4%2A10%2A21%29%29%2F%2820%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+=+%2841+%2B-+sqrt%28+1681-840%29%29%2F%2820%29+ ALIGN=MIDDLE  ALT=\"x+=+%2841+%2B-+sqrt%28+1681-840%29%29%2F%2820%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+=+%2841+%2B-+sqrt%28+841%29%29%2F%2820%29+ ALIGN=MIDDLE  ALT=\"x+=+%2841+%2B-+sqrt%28+841%29%29%2F%2820%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+=+%2841+%2B-+29%29%2F%2820%29+ ALIGN=MIDDLE  ALT=\"x+=+%2841+%2B-+29%29%2F%2820%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+=+%2841+%2B+29%29%2F%2820%29=70%2F20=7%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2841+%2B+29%29%2F%2820%29=70%2F20=7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------larger number<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29=7%2F2-4%2F2=3%2F2 ALIGN=MIDDLE  ALT=\"%28x-2%29=7%2F2-4%2F2=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------------------smaller number<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2841-29%29%2F%2820%29=12%2F20=3%2F5 ALIGN=MIDDLE  ALT=\"x+=+%2841-29%29%2F%2820%29=12%2F20=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29=3%2F5-10%2F5=-7%2F5 ALIGN=MIDDLE  ALT=\"%28x-2%29=3%2F5-10%2F5=-7%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >------------------------NO! NEGATIVE #\r<BR>\n" );
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document.write( " Now we need to test our answer: (7/2 and 3/2)\r<BR>\n" );
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document.write( "2/7+2/3=20/21<BR>\n" );
document.write( "6/21 + 14/21=20/21<BR>\n" );
document.write( "20/21=20/21\r<BR>\n" );
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document.write( "Hope this helps---ptaylor \r<BR>\n" );
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