document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197025>Question 197025</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x^(2)+1/x^(2)=4, then what does x^(3)+1/x^(3) equal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147730 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=147730\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2  +1/x^2 = 4<BR>\n" );
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document.write( "(x^4 +1) / x^2 =4<BR>\n" );
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document.write( "x^4 +1 =4x^2<BR>\n" );
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document.write( "x^4 -4x^2 +1 =0<BR>\n" );
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document.write( "Let  y=x^2<BR>\n" );
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document.write( "y^2 -4y +1 =0<BR>\n" );
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document.write( "using  quadratic  eqn<BR>\n" );
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document.write( "y = { -(-4) +/- sqrt (16-4)} / 2<BR>\n" );
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document.write( "y = 2 +/- sqrt3<BR>\n" );
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document.write( "but  y=x^2<BR>\n" );
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document.write( "x^2 =2+/- sqrt3 =2+/- 1.732 = 3.732, .268<BR>\n" );
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document.write( "x= 1.932, .518<BR>\n" );
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document.write( "Returning  to  x^3 + 1/x^3 = ?<BR>\n" );
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document.write( "1.932 ^3 + 1/ 1.932^3 = 7.35<BR>\n" );
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document.write( "using  .518  gives  same  answer   </SPAN>\n" );
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