document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071835>Question 1071835</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the squares of six consecutive positive even integers is 8284. What are the six numbers? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704822 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=704822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>The answers posted so far both let one of the 6 numbers be x, or 2x.  That leads to solving a quadratic equation that involves an x term.  The algebra is easier if you let the two \"middle\" numbers be x-1 and x+1; that way, when you add the expressions for the squares of the 6 numbers, the x terms all cancel out, making the solution much easier.<br><BR>\n" );
document.write( "So let the 6 numbers be x-5, x-3, x-1, x+1, x+3, and x+5.  Then the sum of the squares is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-10x%2B25%29%2B%28x%5E2-6x%2B9%29%2B%28x%5E2-2x%2B1%29%2B%28x%5E2%2B2x%2B1%29%2B%28x%5E2%2B6x%2B9%29%2B%28x%5E2%2B10x%2B25%29=6x%5E2%2B70 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B70=8284 ALIGN=MIDDLE  ALT=\"6x%5E2%2B70=8284\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2=8214 ALIGN=MIDDLE  ALT=\"6x%5E2=8214\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1369 ALIGN=MIDDLE  ALT=\"x%5E2=1369\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=37 ALIGN=MIDDLE  ALT=\"x=37\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And so the 6 numbers are 32, 34, 36, 38, 40, and 42. </SPAN>\n" );
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