document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116046>Question 116046</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of the square of 2 consecutive odd positive integers is 209. 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 #84402 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If one of the integers is n, then the other one is n + 2, and their squares are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"%28n%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then the sum of the squares is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B%28n%2B2%29%5E2=209 ALIGN=MIDDLE  ALT=\"n%5E2%2B%28n%2B2%29%5E2=209\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand the binomial and simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn%5E2%2B4n%2B4=209 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn%5E2%2B4n%2B4=209\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%5E2%2B4n%2B4=209 ALIGN=MIDDLE  ALT=\"2n%5E2%2B4n%2B4=209\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%5E2%2B4n-205=0 ALIGN=MIDDLE  ALT=\"2n%5E2%2B4n-205=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and now you have a problem because this equation does not have rational roots, which means there is no solution to the problem as you stated it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "However, not being satisfied with that result, I did a little 'easter-egging' and discovered that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%5E2%2B13%5E2=290 ALIGN=MIDDLE  ALT=\"11%5E2%2B13%5E2=290\"   DISABLED_style= \"max-width:90%; height:auto;\" > and concluded that you made a small typographical error when you typed the problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, let's start over:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If one of the integers is n, then the other one is n + 2, and their squares are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2 ALIGN=MIDDLE  ALT=\"n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"%28n%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then the sum of the squares is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B%28n%2B2%29%5E2=290 ALIGN=MIDDLE  ALT=\"n%5E2%2B%28n%2B2%29%5E2=290\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand the binomial and simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2Bn%5E2%2B4n%2B4=290 ALIGN=MIDDLE  ALT=\"n%5E2%2Bn%5E2%2B4n%2B4=290\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%5E2%2B4n%2B4=290 ALIGN=MIDDLE  ALT=\"2n%5E2%2B4n%2B4=290\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n%5E2%2B4n-286=0 ALIGN=MIDDLE  ALT=\"2n%5E2%2B4n-286=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n-143=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n-143=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B13%29%28n-11%29=0 ALIGN=MIDDLE  ALT=\"%28n%2B13%29%28n-11%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So n = 11 or n = -13.  But we can eliminate the -13 result because we are looking for consecutive odd POSITIVE integers.  Therefore, the first integer is 11 and the second is 11 + 2, or 13.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Please be careful and review your input for accuracy in the future. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hope that helps,<BR>\n" );
document.write( "John\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );