document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622302>Question 622302</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hello sir/madam i am shreya from new delhi i want to ask if a,b,c are all non zero and a+b+c=0 prove that a^square/bc+b^square/ca+c^square/ab=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #391321 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=391321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There may be a simpler way for this but here goes...<br><BR>\n" );
document.write( "If<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc+=+0 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%2Bc%29%5E3+=+0 ALIGN=MIDDLE  ALT=\"%28a%2Bb%2Bc%29%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To cube the left side I am going to use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E3+=+x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E3+=+x%5E3%2B3x%5E2y%2B3xy%5E2%2By%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern with the \"x\" being \"(a+b)\" and the \"y\" being \"c\":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E3+%2B+3%28a%2Bb%29%5E2%2Ac+%2B+3%28a%2Bb%29%2Ac%5E2+%2Bc%5E3+=+0 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E3+%2B+3%28a%2Bb%29%5E2%2Ac+%2B+3%28a%2Bb%29%2Ac%5E2+%2Bc%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E3 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > I will use this pattern again:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+%2B+3a%5E2b+%2B3ab%5E2+%2Bb%5E3+%2B+3%28a%2Bb%29%5E2%2Ac+%2B+3%28a%2Bb%29%2Ac%5E2+%2Bc%5E3+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > I will use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E2+=+x%5E2%2B2xy%2By%5E2 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E2+=+x%5E2%2B2xy%2By%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > pattern:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+%2B+3a%5E2b+%2B3ab%5E2+%2Bb%5E3+%2B+3%28a%5E2%2B2ab%2Bb%5E2%29%2Ac+%2B+3%28a%2Bb%29%2Ac%5E2+%2Bc%5E3+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+%2B+3a%5E2b+%2B3ab%5E2+%2Bb%5E3+%2B+3a%5E2%2Ac%2B6abc%2B3b%5E2%2Ac+%2B+3ac%5E2%2B3bc%5E2+%2Bc%5E3+=+0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Next I'll isolate the cubed terms on the left side by subtracting all the non-cubed terms from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+%2Bb%5E3+%2Bc%5E3+=+-3a%5E2b+-3ab%5E2+-+3a%5E2%2Ac-6abc-3b%5E2%2Ac+-+3ac%5E2-3bc%5E2 ALIGN=MIDDLE  ALT=\"a%5E3+%2Bb%5E3+%2Bc%5E3+=+-3a%5E2b+-3ab%5E2+-+3a%5E2%2Ac-6abc-3b%5E2%2Ac+-+3ac%5E2-3bc%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Factoring out -3 on the right side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3+%2Bb%5E3+%2Bc%5E3+=+-3%28a%5E2b+%2Bab%5E2+%2Ba%5E2%2Ac%2B2abc%2Bb%5E2%2Ac+%2Bac%5E2%2Bbc%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Dividing both sides by abc. (We're told that a b and c are all non-zero so it is OK to divide by this.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3+%2Bb%5E3+%2Bc%5E3%29%2Fabc+=+-3%28%28a%5E2b+%2Bab%5E2+%2Ba%5E2%2Ac%2B2abc%2Bb%5E2%2Ac+%2Bac%5E2%2Bbc%5E2%29%2Fabc%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Splitting up the fractions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2Fabc+%2Bb%5E3%2Fabc+%2Bc%5E3%2Fabc+=+-3%28a%5E2b%2Fabc+%2Bab%5E2%2Fabc+%2Ba%5E2%2Ac%2Fabc%2B2abc%2Fabc%2Bb%5E2%2Ac%2Fabc+%2Bac%5E2%2Fabc%2Bbc%5E2%2Fabc%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying the fractions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Fbc+%2Bb%5E2%2Fac+%2Bc%5E2%2Fab+=+-3%28a%2Fc+%2Bb%2Fc+%2Ba%2Fb%2B2%2Bb%2Fa+%2Bc%2Fb%2Bc%2Fa%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Note that the left side is the expression we hope is equal to 3.) Adding the like fractions on the right side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Fbc+%2Bb%5E2%2Fac+%2Bc%5E2%2Fab+=+-3%28%28a%2Bb%29%2Fc+%2B%28a%2Bc%29%2Fb%2B2%2B+%28b%2Bc%29%2Fa%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From a + b + c = 0:<ul><li>Subtracting c from each side we get: a + b = -c</li><li>Subtracting b from each side we get: a + c = -b</li><li>Subtracting a from each side we get: b + c = -a</li></ul>Substituting these expressions in for the numerators on the right side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Fbc+%2Bb%5E2%2Fac+%2Bc%5E2%2Fab+=+-3%28%28-c%29%2Fc+%2B%28-b%29%2Fb%2B2%2B+%28-a%29%2Fa%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying the fractions further:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Fbc+%2Bb%5E2%2Fac+%2Bc%5E2%2Fab+=+-3%28-1+%2B+%28-1%29%2B+2%2B+%28-1%29%29 ALIGN=MIDDLE  ALT=\"a%5E2%2Fbc+%2Bb%5E2%2Fac+%2Bc%5E2%2Fab+=+-3%28-1+%2B+%28-1%29%2B+2%2B+%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Fbc+%2Bb%5E2%2Fac+%2Bc%5E2%2Fab+=+-3%28-1%29 ALIGN=MIDDLE  ALT=\"a%5E2%2Fbc+%2Bb%5E2%2Fac+%2Bc%5E2%2Fab+=+-3%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Fbc+%2Bb%5E2%2Fac+%2Bc%5E2%2Fab+=+3 ALIGN=MIDDLE  ALT=\"a%5E2%2Fbc+%2Bb%5E2%2Fac+%2Bc%5E2%2Fab+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );