document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143178>Question 1143178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the sum of the real solutions of the equation (x+1)(x^2 + 1)(x^3 + 1)=30x^3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763950 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%2B1%29%28x%5E2+%2B+1%29%28x%5E3+%2B+1%29=30x%5E3 ALIGN=MIDDLE  ALT=\"+%28x%2B1%29%28x%5E2+%2B+1%29%28x%5E3+%2B+1%29=30x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E3+%2B+x%5E2+%2B+x+%2B+1%29%28x%5E3+%2B+1%29=30x%5E3 ALIGN=MIDDLE  ALT=\"+%28x%5E3+%2B+x%5E2+%2B+x+%2B+1%29%28x%5E3+%2B+1%29=30x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E6+%2B+x%5E5+%2B+x%5E4+%2B+2+x%5E3+%2B+x%5E2+%2B+x+%2B+1=30x%5E3 ALIGN=MIDDLE  ALT=\"+x%5E6+%2B+x%5E5+%2B+x%5E4+%2B+2+x%5E3+%2B+x%5E2+%2B+x+%2B+1=30x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E6+%2B+x%5E5+%2B+x%5E4+%2B+2+x%5E3+%2B+x%5E2+%2B+x+%2B+1-30x%5E3=0 ALIGN=MIDDLE  ALT=\"+x%5E6+%2B+x%5E5+%2B+x%5E4+%2B+2+x%5E3+%2B+x%5E2+%2B+x+%2B+1-30x%5E3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E6+%2B+x%5E5+%2B+x%5E4+-+28+x%5E3+%2B+x%5E2+%2B+x+%2B+1=0 ALIGN=MIDDLE  ALT=\"+x%5E6+%2B+x%5E5+%2B+x%5E4+-+28+x%5E3+%2B+x%5E2+%2B+x+%2B+1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+3+x+%2B+1%29+%28x%5E4+%2B+4+x%5E3+%2B+12+x%5E2+%2B+4+x+%2B+1%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+3+x+%2B+1%29+%28x%5E4+%2B+4+x%5E3+%2B+12+x%5E2+%2B+4+x+%2B+1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+3+x+%2B+1%29+=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+3+x+%2B+1%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....use quadratic formula to ind solutions\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3 ALIGN=MIDDLE  ALT=\"b=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=1 ALIGN=MIDDLE  ALT=\"c=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%28+9-4+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+9-4+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283+%2B-+sqrt%28+5+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%283+%2B-+sqrt%28+5+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "real solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+3%2F2+-+sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+3%2F2+-+sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B+4+x%5E3+%2B+12+x%5E2+%2B+4+x+%2B+1=0 ALIGN=MIDDLE  ALT=\"x%5E4+%2B+4+x%5E3+%2B+12+x%5E2+%2B+4+x+%2B+1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > you will get only complex solutions; so, disregard it\r<BR>\n" );
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document.write( "the sum of the real solutions will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Bx%5B2%5D+=+3%2F2+%2B+sqrt%285%29%2F2%2B3%2F2+-+sqrt%285%29%2F2 ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Bx%5B2%5D+=+3%2F2+%2B+sqrt%285%29%2F2%2B3%2F2+-+sqrt%285%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Bx%5B2%5D+=+3%2F2+%2B+cross%28sqrt%285%29%2F2%29%2B3%2F2+-+cross%28sqrt%285%29%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Bx%5B2%5D+=+3%2F2+%2B3%2F2+ ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Bx%5B2%5D+=+3%2F2+%2B3%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Bx%5B2%5D+=+6%2F2+ ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Bx%5B2%5D+=+6%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2Bx%5B2%5D+=+3+ ALIGN=MIDDLE  ALT=\"x%5B1%5D%2Bx%5B2%5D+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> your answer\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );