document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=540359>Question 540359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two numbers is 16/15 and the second number is 1 larger thank the first. Find the two numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #353673 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=353673\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The two numbers can be defined as:<BR>\n" );
document.write( "x<BR>\n" );
document.write( "x+1<BR>\n" );
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document.write( "so their reciprocals are:<BR>\n" );
document.write( "1/x<BR>\n" );
document.write( "1/(x+1)<BR>\n" );
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document.write( "1/x + 1/(x+1) = 16/15<BR>\n" );
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document.write( "((x+1)+x)/(x*(x+1) = 16/15<BR>\n" );
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document.write( "15((x+1)+x) = 16(x*(x+1))<BR>\n" );
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document.write( "15x + 15 + 15x = 16(x^2 +x)<BR>\n" );
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document.write( "30x + 15 = 16x^2 +16x<BR>\n" );
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document.write( "0 = 16x^2 -14x -15<BR>\n" );
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document.write( "16x^2 -14x -15 = 0<BR>\n" );
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document.write( "(16x+10)(x-3/2) = 0<BR>\n" );
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document.write( "Check with FOIL.<BR>\n" );
document.write( "16x^2 -24x +10x -15<BR>\n" );
document.write( "Correct<BR>\n" );
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document.write( "So, x = -5/8 or x=3/2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28500%2C500%2C-5%2C5%2C-20%2C20%2C16%2Ax%5E2-14%2Ax-15%29+ ALIGN=MIDDLE  ALT=\"+graph%28500%2C500%2C-5%2C5%2C-20%2C20%2C16%2Ax%5E2-14%2Ax-15%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Or you could solve with quadratic equation.<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=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=16x%5E2%2B-14x%2B-15+=+0 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-14x%2B-15+=+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=%28-14%29%5E2-4%2A16%2A-15=1156 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-14%29%5E2-4%2A16%2A-15=1156\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1156 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--14%2B-sqrt%28+1156+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--14%2B-sqrt%28+1156+%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-%28-14%29%2Bsqrt%28+1156+%29%29%2F2%5C16+=+1.5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+1156+%29%29%2F2%5C16+=+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-%28-14%29-sqrt%28+1156+%29%29%2F2%5C16+=+-0.625 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-14%29-sqrt%28+1156+%29%29%2F2%5C16+=+-0.625\"   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=16x%5E2%2B-14x%2B-15 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-14x%2B-15\"   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=16x%5E2%2B-14x%2B-15+=+16%28x-1.5%29%2A%28x--0.625%29 ALIGN=MIDDLE  ALT=\"16x%5E2%2B-14x%2B-15+=+16%28x-1.5%29%2A%28x--0.625%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.5, -0.625.\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+16%2Ax%5E2%2B-14%2Ax%2B-15+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-14%2Ax%2B-15+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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