document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=178957>Question 178957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sume of the reciprocals of two consecutive odd integers is 20/99.  Find the integers.\r<BR>\n" );
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document.write( "A plane and a truck leave the same town at sunrise and head for a town 450 miles away.  The spead of the plane is 3 times the speed of the truck, and the plane arrives 6 hours ahead of the truck.  Find the speed of the plane.\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 #133903 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=133903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the integers be a and a+2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fa%29%2B%281%2F%28a%2B2%29%29=20%2F99 ALIGN=MIDDLE  ALT=\"%281%2Fa%29%2B%281%2F%28a%2B2%29%29=20%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B2%2Ba%29%2Fa%28a%2B2%29=20%2F99 ALIGN=MIDDLE  ALT=\"%28a%2B2%2Ba%29%2Fa%28a%2B2%29=20%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282a%2B2%29%2F%28a%5E2%2B2a%29=20%2F99 ALIGN=MIDDLE  ALT=\"%282a%2B2%29%2F%28a%5E2%2B2a%29=20%2F99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=198a%2B198=20a%5E2%2B40a ALIGN=MIDDLE  ALT=\"198a%2B198=20a%5E2%2B40a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20a%5E2-158a-198=0 ALIGN=MIDDLE  ALT=\"20a%5E2-158a-198=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=9%29 ALIGN=MIDDLE  ALT=\"highlight%28a=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-1.1 is thrown out<BR>\n" );
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document.write( "integers are:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%289%2C11%29 ALIGN=MIDDLE  ALT=\"system%289%2C11%29\"   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=20x%5E2%2B-158x%2B-198+=+0 ALIGN=MIDDLE  ALT=\"20x%5E2%2B-158x%2B-198+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
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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" );
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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" );
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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=%28-158%29%5E2-4%2A20%2A-198=40804 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-158%29%5E2-4%2A20%2A-198=40804\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=40804 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--158%2B-sqrt%28+40804+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--158%2B-sqrt%28+40804+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-158%29%2Bsqrt%28+40804+%29%29%2F2%5C20+=+9 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-158%29%2Bsqrt%28+40804+%29%29%2F2%5C20+=+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-%28-158%29-sqrt%28+40804+%29%29%2F2%5C20+=+-1.1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-158%29-sqrt%28+40804+%29%29%2F2%5C20+=+-1.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x%5E2%2B-158x%2B-198 ALIGN=MIDDLE  ALT=\"20x%5E2%2B-158x%2B-198\"   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=20x%5E2%2B-158x%2B-198+=+%28x-9%29%2A%28x--1.1%29 ALIGN=MIDDLE  ALT=\"20x%5E2%2B-158x%2B-198+=+%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+20%2Ax%5E2%2B-158%2Ax%2B-198+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+20%2Ax%5E2%2B-158%2Ax%2B-198+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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