document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130446>Question 1130446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve and verify your answer. \r<BR>\n" );
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document.write( "The sum of the reciprocals of two consecutive even integers is 9 / 40. Find the integers (smaller and larger integers). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747128 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=747128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve and verify your answer. <BR>\n" );
document.write( "The sum of the reciprocals of two consecutive even integers is 9 / 40.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fn ALIGN=MIDDLE  ALT=\"1%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28%28n%2B2%29%29 ALIGN=MIDDLE  ALT=\"1%2F%28%28n%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F40 ALIGN=MIDDLE  ALT=\"9%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the integers (smaller and larger integers).<BR>\n" );
document.write( "multiply equation by 40n(n+2), cancel the denominators<BR>\n" );
document.write( "40(n+2) + 40n = 9n(n+2)<BR>\n" );
document.write( "40n + 80 + 40n = 9n^2 + 18n <BR>\n" );
document.write( "80n + 80 = n^2 + 18n<BR>\n" );
document.write( "Form a quadratic equation on the right<BR>\n" );
document.write( "0 = 9n^2 + 18n - 80n - 80<BR>\n" );
document.write( "n^2 - 62 - 80 = 0<BR>\n" );
document.write( "Use the quadratic formula a=9; b=-62; c=-80<BR>\n" );
document.write( "the positive integer solution<BR>\n" );
document.write( "n = 8, and therefore 10 are the integers<BR>\n" );
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document.write( ":\r<BR>\n" );
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document.write( "see if that works<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8 ALIGN=MIDDLE  ALT=\"1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10 ALIGN=MIDDLE  ALT=\"1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( "common denominator is 40<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F40 ALIGN=MIDDLE  ALT=\"5%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F40 ALIGN=MIDDLE  ALT=\"4%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F40 ALIGN=MIDDLE  ALT=\"9%2F40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );