document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209738>Question 1209738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let r, s, and t be solutions of the equation 3x^3 - 4x^2 - 2x + 12 = 0.  Compute<BR>\n" );
document.write( "\frac{rs}{t^2} + \frac{rt}{s^2} + \frac{st}{r^2}. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851885 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52852)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Let r, s, and t be solutions of the equation 3x^3 - 4x^2 - 2x + 12 = 0.  <BR>\n" );
document.write( "Compute (rs)/t^2 + (rt)/s^2 + (st)/r^2.<BR>\n" );
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document.write( "The solution by &nbsp;@CPhill to this problem is &nbsp;INCORRECT.\r<BR>\n" );
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document.write( "The error is when he transforms the formula\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;r³s³ + r³t³ + s³t³ - 3(-4)² = (-2/3)[(rs)² + (rt)² + (st)² - r²st - rs²t - rst²]\r<BR>\n" );
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document.write( "into formula\r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;r³s³ + r³t³ + s³t³ - 48 = (-2/3)[(rs)² + (rt)² + (st)² - rt(rs + st + rt)]\r<BR>\n" );
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document.write( "Indeed, &nbsp;the previous formula is symmetric relative r, s, t, &nbsp;while the last formula is not symmetric.\r<BR>\n" );
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document.write( "Hence, &nbsp;everything which follows makes no sense and is irrelevant.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Honestly, &nbsp;I don't know what is the sense in solving such problems.\r<BR>\n" );
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document.write( "The idea is always the same: &nbsp;use the Vieta's formulas.\r<BR>\n" );
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document.write( "If you know this idea, &nbsp;the rest is simply arithmetic and many-line transformations of formulas.\r<BR>\n" );
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document.write( "Such problems are useful and educative in low degrees.\r<BR>\n" );
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document.write( "In high degrees they become non-sensical tedious exercises.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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