document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105128>Question 105128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Z + 1/Z = 1\r<BR>\n" );
document.write( "\n" );
document.write( "Z ^64 + 1/ Z^64 = ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #76518 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=76518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First off, I'm changing variables because 2 and Z look too much alike and it gets confusing trying to follow. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+%2B+1%2Fu+=+1 ALIGN=MIDDLE  ALT=\"u+%2B+1%2Fu+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%2B1%2Fu%29%5E2 ALIGN=MIDDLE  ALT=\"%28u%2B1%2Fu%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%2B1%2Fu%29%5E2=%28u%2B1%2Fu%29%28u%2B1%2Fu%29 ALIGN=MIDDLE  ALT=\"%28u%2B1%2Fu%29%5E2=%28u%2B1%2Fu%29%28u%2B1%2Fu%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the FOIL method<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%2B1%2Fu%29%5E2=u%5E2%2Bu%281%2Fu%29%2B%281%2Fu%29u%2B1%2Fu%5E2 ALIGN=MIDDLE  ALT=\"%28u%2B1%2Fu%29%5E2=u%5E2%2Bu%281%2Fu%29%2B%281%2Fu%29u%2B1%2Fu%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%2B1%2Fu%29%5E2=u%5E2%2B2%2B1%2Fu%5E2 ALIGN=MIDDLE  ALT=\"%28u%2B1%2Fu%29%5E2=u%5E2%2B2%2B1%2Fu%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But from your original equation, you know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%2B1%2Fu%29=1 ALIGN=MIDDLE  ALT=\"%28u%2B1%2Fu%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28u%2B1%2Fu%29%29%5E2=u%5E2%2B2%2B1%2Fu%5E2 ALIGN=MIDDLE  ALT=\"highlight%28%28u%2B1%2Fu%29%29%5E2=u%5E2%2B2%2B1%2Fu%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%281%29%5E2=u%5E2%2B2%2B1%2Fu%5E2 ALIGN=MIDDLE  ALT=\"highlight%281%29%5E2=u%5E2%2B2%2B1%2Fu%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2%2B1%2Fu%5E2=-1 ALIGN=MIDDLE  ALT=\"u%5E2%2B1%2Fu%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next, look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%5E2%2B1%2Fu%5E2%29%5E2 ALIGN=MIDDLE  ALT=\"%28u%5E2%2B1%2Fu%5E2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%5E2%2B1%2Fu%5E2%29%5E2=%28u%5E2%2B1%2Fu%5E2%29%28u%5E2%2B1%2Fu%5E2%29 ALIGN=MIDDLE  ALT=\"%28u%5E2%2B1%2Fu%5E2%29%5E2=%28u%5E2%2B1%2Fu%5E2%29%28u%5E2%2B1%2Fu%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the FOIL method<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%5E2%2B1%2Fu%5E2%29%5E2=u%5E4%2Bu%5E2%281%2Fu%5E2%29%2B%281%2Fu%5E2%29u%5E2%2B1%2Fu%5E4 ALIGN=MIDDLE  ALT=\"%28u%5E2%2B1%2Fu%5E2%29%5E2=u%5E4%2Bu%5E2%281%2Fu%5E2%29%2B%281%2Fu%5E2%29u%5E2%2B1%2Fu%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%5E2%2B1%2Fu%5E2%29%5E2=u%5E4%2B2%2B1%2Fu%5E4 ALIGN=MIDDLE  ALT=\"%28u%5E2%2B1%2Fu%5E2%29%5E2=u%5E4%2B2%2B1%2Fu%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From 1 you know,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2%2B1%2Fu%5E2=-1 ALIGN=MIDDLE  ALT=\"u%5E2%2B1%2Fu%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28u%5E2%2B1%2Fu%5E2%29%29%5E2=u%5E4%2B2%2B1%2Fu%5E4 ALIGN=MIDDLE  ALT=\"highlight%28%28u%5E2%2B1%2Fu%5E2%29%29%5E2=u%5E4%2B2%2B1%2Fu%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28-1%29%29%5E2=u%5E4%2B2%2B1%2Fu%5E4 ALIGN=MIDDLE  ALT=\"highlight%28%28-1%29%29%5E2=u%5E4%2B2%2B1%2Fu%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=u%5E4%2B2%2B1%2Fu%5E4 ALIGN=MIDDLE  ALT=\"1=u%5E4%2B2%2B1%2Fu%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E4%2B1%2Fu%5E4=-1 ALIGN=MIDDLE  ALT=\"u%5E4%2B1%2Fu%5E4=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You see a pattern here. <BR>\n" );
document.write( "Next, look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%5E4%2B1%2Fu%5E4%29%5E2 ALIGN=MIDDLE  ALT=\"%28u%5E4%2B1%2Fu%5E4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%5E4%2B1%2Fu%5E4%29%5E2=%28u%5E4%2B1%2Fu%5E4%29%28u%5E4%2B1%2Fu%5E4%29 ALIGN=MIDDLE  ALT=\"%28u%5E4%2B1%2Fu%5E4%29%5E2=%28u%5E4%2B1%2Fu%5E4%29%28u%5E4%2B1%2Fu%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%5E4%2B1%2Fu%5E4%29%5E2=u%5E8%2Bu%5E4%281%2Fu%5E4%29%2B%281%2Fu%5E4%29u%5E4%2B1%2Fu%5E8 ALIGN=MIDDLE  ALT=\"%28u%5E4%2B1%2Fu%5E4%29%5E2=u%5E8%2Bu%5E4%281%2Fu%5E4%29%2B%281%2Fu%5E4%29u%5E4%2B1%2Fu%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%5E4%2B1%2Fu%5E4%29%5E2=u%5E8%2B2%2B1%2Fu%5E8 ALIGN=MIDDLE  ALT=\"%28u%5E4%2B1%2Fu%5E4%29%5E2=u%5E8%2B2%2B1%2Fu%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From 2 you know,<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E4%2B1%2Fu%5E4=-1 ALIGN=MIDDLE  ALT=\"u%5E4%2B1%2Fu%5E4=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28u%5E4%2B1%2Fu%5E4%29%29%5E2=u%5E8%2B2%2B1%2Fu%5E8 ALIGN=MIDDLE  ALT=\"highlight%28%28u%5E4%2B1%2Fu%5E4%29%29%5E2=u%5E8%2B2%2B1%2Fu%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28-1%29%5E2=u%5E8%2B2%2B1%2Fu%5E8 ALIGN=MIDDLE  ALT=\"highlight%28-1%29%5E2=u%5E8%2B2%2B1%2Fu%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=u%5E8%2B2%2B1%2Fu%5E8 ALIGN=MIDDLE  ALT=\"1=u%5E8%2B2%2B1%2Fu%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E8%2B1%2Fu%5E8=-1 ALIGN=MIDDLE  ALT=\"u%5E8%2B1%2Fu%5E8=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's fast forward.<BR>\n" );
document.write( "I'll bet that you can get to this answer by continuing to follow the steps that we followed up until now to get the answer. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E64%2B1%2Fu%5E64=-1 ALIGN=MIDDLE  ALT=\"u%5E64%2B1%2Fu%5E64=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );