document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=641187>Question 641187</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of the reciprocals of two consecutive integers is 7/12. find the two integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #403574 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=403574\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two consecutive even integers. We'll call them <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2 ALIGN=MIDDLE  ALT=\"x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Their reciprocals would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"1%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. They add to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F12 ALIGN=MIDDLE  ALT=\"7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "So we have the following equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx+%2B+1%2F%28x+%2B+2%29+=+7%2F12 ALIGN=MIDDLE  ALT=\"1%2Fx+%2B+1%2F%28x+%2B+2%29+=+7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x+%2B+2%29+%2B+x%29+%2F+%28x%28x+%2B+2%29%29+=+7%2F12 ALIGN=MIDDLE  ALT=\"%28%28x+%2B+2%29+%2B+x%29+%2F+%28x%28x+%2B+2%29%29+=+7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x+%2B+2%29+%2F+%28x%5E2+%2B+2x%29+=+7%2F12 ALIGN=MIDDLE  ALT=\"%282x+%2B+2%29+%2F+%28x%5E2+%2B+2x%29+=+7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%282x+%2B+2%29+=+7%28x%5E2+%2B+2x%29 ALIGN=MIDDLE  ALT=\"12%282x+%2B+2%29+=+7%28x%5E2+%2B+2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24x+%2B+24+=+7x%5E2+%2B+14x ALIGN=MIDDLE  ALT=\"24x+%2B+24+=+7x%5E2+%2B+14x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2-24x+%2B+14x-24=0 ALIGN=MIDDLE  ALT=\"7x%5E2-24x+%2B+14x-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x%5E2-10x-24=0 ALIGN=MIDDLE  ALT=\"7x%5E2-10x-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use quadratic formula to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2A7%2A%28-24%29+%29%29%2F%282%2A7%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2A7%2A%28-24%29+%29%29%2F%282%2A7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28100%2B672%29%29%2F14+ ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28100%2B672%29%29%2F14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28772%29%29%2F14+ ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28772%29%29%2F14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+27.79%29%2F14+ ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+27.79%29%2F14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B+27.79%29%2F14+ ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B+27.79%29%2F14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+37.79%2F14+ ALIGN=MIDDLE  ALT=\"x+=+37.79%2F14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2.7+ ALIGN=MIDDLE  ALT=\"x+=+2.7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+-+27.79%29%2F14+ ALIGN=MIDDLE  ALT=\"x+=+%2810+-+27.79%29%2F14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+17.79%2F14+ ALIGN=MIDDLE  ALT=\"x+=+17.79%2F14+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.27+ ALIGN=MIDDLE  ALT=\"x+=+1.27+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx+%2B+1%2F%28x+%2B+2%29+=+7%2F12 ALIGN=MIDDLE  ALT=\"1%2Fx+%2B+1%2F%28x+%2B+2%29+=+7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2.7++%2B+1%2F%281.27+%2B+2%29+=+0.6 ALIGN=MIDDLE  ALT=\"1%2F2.7++%2B+1%2F%281.27+%2B+2%29+=+0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.3++%2B+1%2F3.27+=+0.6 ALIGN=MIDDLE  ALT=\"0.3++%2B+1%2F3.27+=+0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.3++%2B+0.3+=+0.6 ALIGN=MIDDLE  ALT=\"0.3++%2B+0.3+=+0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.6+=+0.6 ALIGN=MIDDLE  ALT=\"0.6+=+0.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );