document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204547>Question 1204547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive even integers is 23/264<BR>\n" );
document.write( ". 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 #840860 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=840860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = first even integer<BR>\n" );
document.write( "x+2 = second even integer just after x.\r<BR>\n" );
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document.write( "Their reciprocals add to 23/264.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx+%2B+1%2F%28x%2B2%29+=+23%2F264 ALIGN=MIDDLE  ALT=\"1%2Fx+%2B+1%2F%28x%2B2%29+=+23%2F264\"   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=%28x%2B2%29%2F%28x%28x%2B2%29%29+%2B+x%2F%28x%28x%2B2%29%29+=+23%2F264 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%2F%28x%28x%2B2%29%29+%2B+x%2F%28x%28x%2B2%29%29+=+23%2F264\"   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=%28x%2B2%2Bx%29%2F%28x%28x%2B2%29%29+=+23%2F264 ALIGN=MIDDLE  ALT=\"%28x%2B2%2Bx%29%2F%28x%28x%2B2%29%29+=+23%2F264\"   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%2B2%29%2F%28x%28x%2B2%29%29+=+23%2F264 ALIGN=MIDDLE  ALT=\"%282x%2B2%29%2F%28x%28x%2B2%29%29+=+23%2F264\"   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%2B2%29%2A264+=+x%28x%2B2%29%2A23 ALIGN=MIDDLE  ALT=\"%282x%2B2%29%2A264+=+x%28x%2B2%29%2A23\"   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=264%282x%2B2%29+=+23x%28x%2B2%29 ALIGN=MIDDLE  ALT=\"264%282x%2B2%29+=+23x%28x%2B2%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=528x%2B528+=+23x%5E2%2B46x ALIGN=MIDDLE  ALT=\"528x%2B528+=+23x%5E2%2B46x\"   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+=+23x%5E2%2B46x-528x-528 ALIGN=MIDDLE  ALT=\"0+=+23x%5E2%2B46x-528x-528\"   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=23x%5E2-482x-528+=+0 ALIGN=MIDDLE  ALT=\"23x%5E2-482x-528+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the quadratic formula from here.<BR>\n" );
document.write( "a = 23, b = -482, c = -528<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%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-%28-482%29%2B-sqrt%28%28-482%29%5E2-4%2823%29%28-528%29%29%29%2F%282%2823%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-482%29%2B-sqrt%28%28-482%29%5E2-4%2823%29%28-528%29%29%29%2F%282%2823%29%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+=+%28482%2B-sqrt%28232324+%2B+-48576%29%29%2F%2846%29 ALIGN=MIDDLE  ALT=\"x+=+%28482%2B-sqrt%28232324+%2B+-48576%29%29%2F%2846%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+=+%28482%2B-sqrt%28280900%29%29%2F%2846%29 ALIGN=MIDDLE  ALT=\"x+=+%28482%2B-sqrt%28280900%29%29%2F%2846%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+=+%28482%2B-++530%29%2F%2846%29 ALIGN=MIDDLE  ALT=\"x+=+%28482%2B-++530%29%2F%2846%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+=+%28482%2B530%29%2F%2846%29 ALIGN=MIDDLE  ALT=\"x+=+%28482%2B530%29%2F%2846%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28482-530%29%2F%2846%29 ALIGN=MIDDLE  ALT=\"x+=+%28482-530%29%2F%2846%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+=+%281012%29%2F%2846%29 ALIGN=MIDDLE  ALT=\"x+=+%281012%29%2F%2846%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-48%29%2F%2846%29 ALIGN=MIDDLE  ALT=\"x+=+%28-48%29%2F%2846%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+=+22 ALIGN=MIDDLE  ALT=\"x+=+22\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-24%2F23 ALIGN=MIDDLE  ALT=\"x+=+-24%2F23\"   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+=+22 ALIGN=MIDDLE  ALT=\"x+=+22\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%281%2C2%2Cx+=+-1.043478%2C%22approximately%22%29 ALIGN=MIDDLE  ALT=\"matrix%281%2C2%2Cx+=+-1.043478%2C%22approximately%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Ignore the non-integer result.\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F22+%2B+1%2F24+=+23%2F264 ALIGN=MIDDLE  ALT=\"1%2F22+%2B+1%2F24+=+23%2F264\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer: The two consecutive even integers are <font color=red>22 and 24</font>.<BR>\n" );
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