document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=637638>Question 637638</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the product of two consecutive even numbers is 36 times more than the square of the smaller number.find the consecutive numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401786 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=401786\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Strange wording. There may be a typo. I have two interpretations.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If the problem really meant to say that the product is \"36 times the square of the smaller number\", which is 36 multiplied times the smaller number, then the smaller number is zero.<BR>\n" );
document.write( "With the two consecutive even (integer) numbers represented as n and n+2, the math would be:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B2%29=36n%5E2 ALIGN=MIDDLE  ALT=\"n%28n%2B2%29=36n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n=36n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n=36n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n-n%5E2-2n=36n%5E2-n%5E2-2n ALIGN=MIDDLE  ALT=\"n%5E2%2B2n-n%5E2-2n=36n%5E2-n%5E2-2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=36n%5E2-n%5E2-2n ALIGN=MIDDLE  ALT=\"0=36n%5E2-n%5E2-2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=35n%5E2-2n ALIGN=MIDDLE  ALT=\"0=35n%5E2-2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%2835n-2%29n ALIGN=MIDDLE  ALT=\"0=%2835n-2%29n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions to that equation are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2%2F35 ALIGN=MIDDLE  ALT=\"n=2%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > , from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35n-2=0 ALIGN=MIDDLE  ALT=\"35n-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35n=2 ALIGN=MIDDLE  ALT=\"35n=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2%2F35 ALIGN=MIDDLE  ALT=\"n=2%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=0 ALIGN=MIDDLE  ALT=\"n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F35 ALIGN=MIDDLE  ALT=\"2%2F35\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not an even integer, the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=0 ALIGN=MIDDLE  ALT=\"n=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, if we consider zero to be even. (I do, but it could be controversial).<BR>\n" );
document.write( " <BR>\n" );
document.write( "If the problem really meant to say that the product is \"36 more than the square of the smaller number\", there should be no \"times\" in the wording.<BR>\n" );
document.write( "In that case, it means that it is 36 added to the square of the smaller number.<BR>\n" );
document.write( "Then, calling the smaller number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > (we'll make sure it's even at the end),<BR>\n" );
document.write( "the next even number would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B2 ALIGN=MIDDLE  ALT=\"n%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the wording translates into the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B2%29=n%5E2%2B36 ALIGN=MIDDLE  ALT=\"n%28n%2B2%29=n%5E2%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n%2B2%29=n%5E2%2B36 ALIGN=MIDDLE  ALT=\"n%28n%2B2%29=n%5E2%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n=n%5E2%2B36 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n=n%5E2%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n-n%5E2=n%5E2%2B36-n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n-n%5E2=n%5E2%2B36-n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n=36 ALIGN=MIDDLE  ALT=\"2n=36\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%2F2=36%2F2 ALIGN=MIDDLE  ALT=\"2n%2F2=36%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=18%29 ALIGN=MIDDLE  ALT=\"highlight%28n=18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is even.<BR>\n" );
document.write( "So the numbers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2818%29 ALIGN=MIDDLE  ALT=\"highlight%2818%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2820%29 ALIGN=MIDDLE  ALT=\"highlight%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );