document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993888>Question 993888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "I don't know if this is the right category, but while gkimming through a question paper i found one question:<BR>\n" );
document.write( "a+b+c=10, find the maximum value possible for (a*b*c)+(a*b)+(b*c)+(a*c).<BR>\n" );
document.write( "Please help me solve this, as this is not just one of it's type in the question paper, there are 5 or 6 such ones. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #613064 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=613064\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a+b+c=10, find the maximum value possible for (a*b*c)+(a*b)+(b*c)+(a*c).<BR>\n" );
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document.write( "Using Excel, I confirmed my suspicion that the max is at a = b = c<BR>\n" );
document.write( "Max = 69967/999<BR>\n" );
document.write( "= 31*61/27<BR>\n" );
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document.write( "27 is obviously 3*3*3, but I don't know the significance of 31 or 61.<BR>\n" );
document.write( "I don't yet have a proof, either. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );