document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=490715>Question 490715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I am having trouble with this question:\r<BR>\n" );
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document.write( "Find all possible sets of 4 consecutive integers such that the sum of the cubes of the smallest three is the cube of the fourth.\r<BR>\n" );
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document.write( "I tried forming an equation:  x^3 + (x+1)^3 + (x+2)^3 = (x + 3)^3<BR>\n" );
document.write( "But then I got stumped.<BR>\n" );
document.write( "Can you please help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #334232 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=334232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Expanding your equation yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^3 + (x^3 + 3x^2 + 3x + 1) + (x^3 + 6x^2 + 12x + 8) = x^3 + 9x^2 + 27x + 27\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 3x^3 + 9x^2 + 15x + 9 = x^3 + 9x^2 + 27x + 27\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 2x^3 - 12x - 18 = 0 \Rightarrow x^3 - 6x - 9 = 0\">\r<BR>\n" );
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document.write( "From here, we can tell that x = 3 works. If you divide both sides of the previous equation by x-3 (either by synthetic or long division) we can find the other two roots:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2 + 3x + 3 = 0\">\r<BR>\n" );
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document.write( "The discriminant is negative, so there are no more integer roots. Hence x=3 --> {3,4,5,6} is the only solution. </SPAN>\n" );
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