document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=696813>Question 696813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find (a, b, c) if<BR>\n" );
document.write( "2a+3b+c=11<BR>\n" );
document.write( "6ab+2ac+3bc=24<BR>\n" );
document.write( "abc=-6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429459 by </B><A HREF=/tutors/aboutme.mpl?userid=god2012><B>god2012(113)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=god2012><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=god2012><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=429459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2a+3b+c=11  ---------------------------------eq.1<BR>\n" );
document.write( "6ab+2ac+3bc=24-------------------------------eq.2<BR>\n" );
document.write( "abc=-6  -------------------------------------eq.3\r<BR>\n" );
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document.write( "From Eq.1 ,  2a+3b = 11 - c<BR>\n" );
document.write( "From eq.2 , 6ab + c (11 - c) = 24<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6ab%2B11c-c%5E2+=+24 ALIGN=MIDDLE  ALT=\"6ab%2B11c-c%5E2+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" >----------------------eq.4\r<BR>\n" );
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document.write( "From eq.3 , ab = -6/c\r<BR>\n" );
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document.write( "Therefore eq.4 becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28-6%2Fc%29%2B11c-c%5E2+=+24 ALIGN=MIDDLE  ALT=\"6%28-6%2Fc%29%2B11c-c%5E2+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36%2B11c%5E2-c%5E3+=+24c ALIGN=MIDDLE  ALT=\"-36%2B11c%5E2-c%5E3+=+24c\"   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=c%5E3-11c%5E2%2B24c%2B36+=+0 ALIGN=MIDDLE  ALT=\"c%5E3-11c%5E2%2B24c%2B36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a cubic equation <BR>\n" );
document.write( "By trial and error , one of the roots of the equation is -1.<BR>\n" );
document.write( "Therefore ,(c-1) is a factor.<BR>\n" );
document.write( "Let us reduce the cubic equation to a quadratic equation.<BR>\n" );
document.write( "We get , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2-12c%2B36 ALIGN=MIDDLE  ALT=\"c%5E2-12c%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the quotient which is a quadratic equation.\r<BR>\n" );
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document.write( "The roots are 6 and 6.<BR>\n" );
document.write( "c = {-1,6}\r<BR>\n" );
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document.write( "Therefore 2a+3b = 11-(-1) = 12 --------------------eq.5<BR>\n" );
document.write( "ab(-1) = -6<BR>\n" );
document.write( "ab = 6<BR>\n" );
document.write( "b  = 6/a\r<BR>\n" );
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document.write( "Substitute for b in eq.5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2B3%286%2Fa%29+=+12 ALIGN=MIDDLE  ALT=\"2a%2B3%286%2Fa%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2%2B18+-12a+=+0 ALIGN=MIDDLE  ALT=\"2a%5E2%2B18+-12a+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a quadratic equation whose roots are 3 and 3\r<BR>\n" );
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document.write( "Therefore , b = 2\r<BR>\n" );
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document.write( "(a,b,c) = (3,2,-1)  when c = -1<BR>\n" );
document.write( "But when  c = 6, we have 2 possibilities for a and b\r<BR>\n" );
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document.write( "(a,b,c) = (3,-1/3,6)  OR (-1/2 , 2,6)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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