document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=857368>Question 857368</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three consecutive integers such that two times the sum of all three is 3 times the product of the larger two. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516993 by </B><A HREF=/tutors/aboutme.mpl?userid=ben720><B>ben720(159)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ben720><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=516993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <BR>\n" );
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document.write( "For three consecutive integers, <BR>\n" );
document.write( "Let X = 1st<BR>\n" );
document.write( "X+1 = 2nd<BR>\n" );
document.write( "X+2 = 3rd<BR>\n" );
document.write( "Therefore, the sum of the three is X+(X+1)+(X+2), or 3X+3 total.<BR>\n" );
document.write( "For the equation, twice the sum is 3 times the product of the larger two, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283X%2B3%29=3%28X%2B1%29%28X%2B2%29 ALIGN=MIDDLE  ALT=\"2%283X%2B3%29=3%28X%2B1%29%28X%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From here, distribute<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6X%2B6=%283X%2B3%29%28X%2B2%29 ALIGN=MIDDLE  ALT=\"6X%2B6=%283X%2B3%29%28X%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, distribute some more...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6X%2B6=3X%5E2%2B9X%2B6 ALIGN=MIDDLE  ALT=\"6X%2B6=3X%5E2%2B9X%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract (6X+6)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=3X%5E2%2B3X%2B0 ALIGN=MIDDLE  ALT=\"0=3X%5E2%2B3X%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, use the quadratic formula to find your two X's<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=%28-3%2B-sqrt%283%5E2-4%2A3%2A0%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"X=%28-3%2B-sqrt%283%5E2-4%2A3%2A0%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Do the appropriate multiplication<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=%28-3%2B-sqrt%289-0%29%29%2F%286%29 ALIGN=MIDDLE  ALT=\"X=%28-3%2B-sqrt%289-0%29%29%2F%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Keep simplifying<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=%28-3%2B3%29%2F6 ALIGN=MIDDLE  ALT=\"X=%28-3%2B3%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=%28-3-3%29%2F6 ALIGN=MIDDLE  ALT=\"X=%28-3-3%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the answer is either<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=%28-3%2B3%29%2F6=0 ALIGN=MIDDLE  ALT=\"X=%28-3%2B3%29%2F6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=%28-3-3%29%2F6=-6%2F6=-1. ALIGN=MIDDLE  ALT=\"X=%28-3-3%29%2F6=-6%2F6=-1.\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And so, the two answers for X are 0 and -1. The second is X + 1, third is X + 2.<BR>\n" );
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document.write( "Your 2 answers are 0, 1, 2 or -1, 0, 1.<BR>\n" );
document.write( " <BR>\n" );
document.write( "To check, plug each of them in:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280%2B1%2B2%29=3%281%2A2%29 ALIGN=MIDDLE  ALT=\"2%280%2B1%2B2%29=3%281%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283%29=3%282%29 ALIGN=MIDDLE  ALT=\"2%283%29=3%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=6 ALIGN=MIDDLE  ALT=\"6=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next, try -1, 0, 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-1%2B0%2B1%29=3%280%2A1%29 ALIGN=MIDDLE  ALT=\"2%28-1%2B0%2B1%29=3%280%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280%29=3%280%29 ALIGN=MIDDLE  ALT=\"2%280%29=3%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " <BR>\n" );
document.write( "Your final, checked answers are 0, 1, and 2; or -1, 0, and 1. <BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );