document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=577760>Question 577760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if x^2 + 1/x^2 =4 , then find the value of x^3 + 1/x^3<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #370286 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=370286\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2 + \frac{1}{x^2} = (x + \frac{1}{x})^2 - 2 = 4\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x + \frac{1}{x})^2 = 6 \Rightarrow x + \frac{1}{x} = \pm \sqrt{6}\">\r<BR>\n" );
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document.write( "Consider the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE (x^2 + \frac{1}{x^2})(x + \frac{1}{x}) = \pm 4 \sqrt{6}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^3 + \frac{1}{x^3} + x + \frac{1}{x} = \pm 4 \sqrt{6}\">\r<BR>\n" );
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document.write( "We know that if x + 1/x is sqrt(6), then we will have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^3 + \frac{1}{x^3} + \sqrt{6} = 4 \sqrt{6} \Rightarrow x^3 + \frac{1}{x^3} = 3 \sqrt{6}\">\r<BR>\n" );
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document.write( "If x + 1/x = -sqrt(6) then we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^3 + \frac{1}{x^3} - \sqrt{6} = -4\sqrt{6} \Rightarrow x^3 + \frac{1}{x^3} = -3\sqrt{6}\">\r<BR>\n" );
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document.write( "Either of these can be correct. </SPAN>\n" );
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