document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142053>Question 1142053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that cos 2pi/9 is a root of the equation 8x^3 - 6x + 1=0  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762717 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762717\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think you meant to say \"Show it is NOT a root.\"<br>\r<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi+ ALIGN=MIDDLE  ALT=\"+pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a transcendental number - which means neither it, nor any rational multiple of it, is the root of ANY polynomial equation with integer coefficients.  <BR>\n" );
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document.write( "It is the very definition of a transcendental number.\r<BR>\n" );
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document.write( "EDIT: Oh, disregard, I just noticed cos in front, you should really write cos(2pi/9)<BR>\n" );
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document.write( "cos(2pi/9) is approx 0.76604444\r<BR>\n" );
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document.write( "Plugging this into the equation gives 0 out, therefore cos(2pi/9) is a root.\r<BR>\n" );
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