document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153004>Question 153004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the equation (x-a)(x-b)+(x-b)(x-c)+(x-a)(x-c)=0 has equal roots when a=b=c </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112478 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=112478\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29%28x-b%29%2B%28x-b%29%28x-c%29%2B%28x-a%29%28x-c%29=0 ALIGN=MIDDLE  ALT=\"%28x-a%29%28x-b%29%2B%28x-b%29%28x-c%29%2B%28x-a%29%28x-c%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29%28x-a%29%2B%28x-a%29%28x-a%29%2B%28x-a%29%28x-a%29=0 ALIGN=MIDDLE  ALT=\"%28x-a%29%28x-a%29%2B%28x-a%29%28x-a%29%2B%28x-a%29%28x-a%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=a ALIGN=MIDDLE  ALT=\"b=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=a ALIGN=MIDDLE  ALT=\"c=a\"   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%5E2-2ax%2Ba%5E2%2Bx%5E2-2ax%2Ba%5E2%2Bx%5E2-2ax%2Ba%5E2=0 ALIGN=MIDDLE  ALT=\"x%5E2-2ax%2Ba%5E2%2Bx%5E2-2ax%2Ba%5E2%2Bx%5E2-2ax%2Ba%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-6ax%2B3a%5E2=0 ALIGN=MIDDLE  ALT=\"3x%5E2-6ax%2B3a%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x-a%29%5E2=0 ALIGN=MIDDLE  ALT=\"3%28x-a%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x-a%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-a=0 ALIGN=MIDDLE  ALT=\"x-a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a ALIGN=MIDDLE  ALT=\"x=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add \"a\" to both sides.\r<BR>\n" );
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document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-a%29%28x-b%29%2B%28x-b%29%28x-c%29%2B%28x-a%29%28x-c%29 ALIGN=MIDDLE  ALT=\"%28x-a%29%28x-b%29%2B%28x-b%29%28x-c%29%2B%28x-a%29%28x-c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a ALIGN=MIDDLE  ALT=\"x=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > (with a multiplicity of 2) if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=b=c ALIGN=MIDDLE  ALT=\"a=b=c\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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