document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=926556>Question 926556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of a number and its reciprocal is 1 3<BR>\n" );
document.write( "_<BR>\n" );
document.write( "6<BR>\n" );
document.write( ". Find<BR>\n" );
document.write( "the number </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #563169 by </B><A HREF=/tutors/aboutme.mpl?userid=srinivas.g><B>srinivas.g(540)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=srinivas.g><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=srinivas.g><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=563169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x be thew number<BR>\n" );
document.write( "its reciprocal is 1/x<BR>\n" );
document.write( " so  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2B%281%2Fx%29=+13%2F6 ALIGN=MIDDLE  ALT=\"+x%2B%281%2Fx%29=+13%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "       L.C.M is x<BR>\n" );
document.write( "      so<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x%2Ax%2B1%29%2Fx++=13%2F6 ALIGN=MIDDLE  ALT=\"+%28+x%2Ax%2B1%29%2Fx++=13%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "            <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2%2B1%29%2Fx+=+13%2F6 ALIGN=MIDDLE  ALT=\"+%28x%5E2%2B1%29%2Fx+=+13%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply with 6 on both sides<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B1%29%2F%28x%29%2A6+=+%2813%2F6%29%2A6 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B1%29%2F%28x%29%2A6+=+%2813%2F6%29%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%5E2%2B6%29%2F%28x%29+=+13 ALIGN=MIDDLE  ALT=\"%286x%5E2%2B6%29%2F%28x%29+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "   multiply with x on both sides<BR>\n" );
document.write( "   <BR>\n" );
document.write( "       <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%5E2%2B6%29%2F%28x%29%2Ax+=+13%2Ax ALIGN=MIDDLE  ALT=\"%286x%5E2%2B6%29%2F%28x%29%2Ax+=+13%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "              <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%5E2%2B6%29=+13%2Ax ALIGN=MIDDLE  ALT=\"%286x%5E2%2B6%29=+13%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-13x%2B6=0 ALIGN=MIDDLE  ALT=\"6x%5E2-13x%2B6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=quadratic.solver>SOLVE quadratic equation with variable</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=6x%5E2%2B-13x%2B6+=+0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B-13x%2B6+=+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=%28-13%29%5E2-4%2A6%2A6=25 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-13%29%5E2-4%2A6%2A6=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=25 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--13%2B-sqrt%28+25+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--13%2B-sqrt%28+25+%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-%28-13%29%2Bsqrt%28+25+%29%29%2F2%5C6+=+1.5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+25+%29%29%2F2%5C6+=+1.5\"   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-%28-13%29-sqrt%28+25+%29%29%2F2%5C6+=+0.666666666666667 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-13%29-sqrt%28+25+%29%29%2F2%5C6+=+0.666666666666667\"   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=6x%5E2%2B-13x%2B6 ALIGN=MIDDLE  ALT=\"6x%5E2%2B-13x%2B6\"   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=6x%5E2%2B-13x%2B6+=+6%28x-1.5%29%2A%28x-0.666666666666667%29 ALIGN=MIDDLE  ALT=\"6x%5E2%2B-13x%2B6+=+6%28x-1.5%29%2A%28x-0.666666666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.5, 0.666666666666667.\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+6%2Ax%5E2%2B-13%2Ax%2B6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-13%2Ax%2B6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );