document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146812>Question 146812</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of the reciprocals of two consecutive odd integers is 20/99. find the two integers.\r<BR>\n" );
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document.write( "pleasee helpp </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107214 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1/n + 1/(n+2) = 20/99<BR>\n" );
document.write( "Multiply by n(n+2)<BR>\n" );
document.write( "n+2 + n = 20n(n+2)/99<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%2B2+=+%2820n%5E2+%2B+40n%29%2F99 ALIGN=MIDDLE  ALT=\"2n%2B2+=+%2820n%5E2+%2B+40n%29%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply by 99<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=198n+%2B+198+=+20n%5E2+%2B+40n ALIGN=MIDDLE  ALT=\"198n+%2B+198+=+20n%5E2+%2B+40n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Put in quadratic form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20n%5E2+-+158n+-+198+=+0 ALIGN=MIDDLE  ALT=\"20n%5E2+-+158n+-+198+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10n%5E2+-+79n+-+99+=+0 ALIGN=MIDDLE  ALT=\"10n%5E2+-+79n+-+99+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2%2B-79x%2B-99+=+0 ALIGN=MIDDLE  ALT=\"10x%5E2%2B-79x%2B-99+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-79%29%5E2-4%2A10%2A-99=10201 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-79%29%5E2-4%2A10%2A-99=10201\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=10201 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--79%2B-sqrt%28+10201+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--79%2B-sqrt%28+10201+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-79%29%2Bsqrt%28+10201+%29%29%2F2%5C10+=+9 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-79%29%2Bsqrt%28+10201+%29%29%2F2%5C10+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-79%29-sqrt%28+10201+%29%29%2F2%5C10+=+-1.1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-79%29-sqrt%28+10201+%29%29%2F2%5C10+=+-1.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2%2B-79x%2B-99 ALIGN=MIDDLE  ALT=\"10x%5E2%2B-79x%2B-99\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10x%5E2%2B-79x%2B-99+=+%28x-9%29%2A%28x--1.1%29 ALIGN=MIDDLE  ALT=\"10x%5E2%2B-79x%2B-99+=+%28x-9%29%2A%28x--1.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 9, -1.1.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B-79%2Ax%2B-99+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B-79%2Ax%2B-99+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "-1.1 is not a positive integer, so discard it.<BR>\n" );
document.write( "n = 9<BR>\n" );
document.write( "n+2 = 11<BR>\n" );
document.write( "It does work, 1/9 + 1/11 = 20/99 </SPAN>\n" );
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