document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=505266>Question 505266</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive even integers a and b is<BR>\n" );
document.write( "7 over 24<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Find the integers.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339858 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339858\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of the reciprocals of two consecutive even integers a and b is<BR>\n" );
document.write( "7 over 24<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Find the integers. <BR>\n" );
document.write( "==============================<BR>\n" );
document.write( "If they are consecutive even integers, and a is the smallest, then b = a + 2<BR>\n" );
document.write( "The sum of the reciprocals = 7/24:<BR>\n" );
document.write( "1/a + 1/(a+2) = 7/24<BR>\n" );
document.write( "((a+2) + a)/(a(a+2)) = 7/24<BR>\n" );
document.write( "(2a+2)/(a^2+2a) = 7/24<BR>\n" );
document.write( "7a^2 - 34a - 48 = 0 [cross multiply and simplify]<BR>\n" );
document.write( "This can be factored:<BR>\n" );
document.write( "(7a+8)(a-6) = 0<BR>\n" );
document.write( "Since the number is an integer, a = 6<BR>\n" );
document.write( "So the other integer = 8<BR>\n" );
document.write( "Ans: 6,8<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "1/6 + 1/8 = (3 + 4)/24 = 7/24 </SPAN>\n" );
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