document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1097613>Question 1097613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If three numbers are consecutive positive integers<BR>\n" );
document.write( "and five times the square of the largest number is<BR>\n" );
document.write( "greater than two times the sum of the squares of<BR>\n" );
document.write( "the other two numbers by 75, then the sum of the<BR>\n" );
document.write( "smallest and the largest of these numbers is<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712054 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=712054\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would call the three consecutive positive integers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-1 ALIGN=MIDDLE  ALT=\"n-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Five times the square of the largest number is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28n%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"5%28n%2B1%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Two times the sum of the squares<BR>\n" );
document.write( "of the other two numbers is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28n%5E2%2B%28n-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"2%28n%5E2%2B%28n-1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "The question states that the first expression above<BR>\n" );
document.write( "is greater than the second one by 75.<BR>\n" );
document.write( "That can be expressed as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28n%2B1%29%5E2=2%28n%5E2%2B%28n-1%29%5E2%29%2B75 ALIGN=MIDDLE  ALT=\"5%28n%2B1%29%5E2=2%28n%5E2%2B%28n-1%29%5E2%29%2B75\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "We can simplify that equation and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If we find one or more solutions that is/are positive and integer,<BR>\n" );
document.write( "we almost have the answer,<BR>\n" );
document.write( "because what we want to find is the sum of the<BR>\n" );
document.write( "smallest and the largest of the three consecutive positive integers,<BR>\n" );
document.write( "and that would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-1%29%2B%28n%2B1%29=n-1%2Bn%2B1=2n ALIGN=MIDDLE  ALT=\"%28n-1%29%2B%28n%2B1%29=n-1%2Bn%2B1=2n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%5E2=2%28n%5E2%2B%28n-1%29%5E2%29%2B75 ALIGN=MIDDLE  ALT=\"%28n%2B1%29%5E2=2%28n%5E2%2B%28n-1%29%5E2%29%2B75\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28n%2B1%29%5E2=2%28n%5E2%2B%28n-1%29%5E2%29%2B75 ALIGN=MIDDLE  ALT=\"5%28n%2B1%29%5E2=2%28n%5E2%2B%28n-1%29%5E2%29%2B75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28n%5E2%2B2n%2B1%29=2%28n%5E2%2Bn%5E2-2n%2B1%29%2B75 ALIGN=MIDDLE  ALT=\"5%28n%5E2%2B2n%2B1%29=2%28n%5E2%2Bn%5E2-2n%2B1%29%2B75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2%2B10n%2B5=2%282n%5E2-2n%2B1%29%2B75 ALIGN=MIDDLE  ALT=\"5n%5E2%2B10n%2B5=2%282n%5E2-2n%2B1%29%2B75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2%2B10n%2B5=4n%5E2-4n%2B2%2B75 ALIGN=MIDDLE  ALT=\"5n%5E2%2B10n%2B5=4n%5E2-4n%2B2%2B75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2%2B10n%2B5=4n%5E2-4n%2B77 ALIGN=MIDDLE  ALT=\"5n%5E2%2B10n%2B5=4n%5E2-4n%2B77\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5n%5E2%2B10n%2B5-4n%5E2%2B4n-77=0 ALIGN=MIDDLE  ALT=\"5n%5E2%2B10n%2B5-4n%5E2%2B4n-77=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%2B14n-72=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B14n-72=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%2B18%29%28n-4%29=0 ALIGN=MIDDLE  ALT=\"%28n%2B18%29%28n-4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28n--18%2C%22or%22%2Cn=4%29 ALIGN=MIDDLE  ALT=\"system%28n--18%2C%22or%22%2Cn=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The  only possible answer comes from the positive integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=4 ALIGN=MIDDLE  ALT=\"n=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2n=2%2A4=highlight%288%29 ALIGN=MIDDLE  ALT=\"2n=2%2A4=highlight%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );