document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=464084>Question 464084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If (x + 1/x) = 1 and (z + 1/z) =1; show that (z + 1/x) =1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317879 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As it stands, the statement is not true.\r<BR>\n" );
document.write( "\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%3C%3Ez+ ALIGN=MIDDLE  ALT=\"+x%3C%3Ez+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then both x and z are the roots of the quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and both roots are complex.  Hence one root is the complex conjugate of the other, by theorem in algebra.  <BR>\n" );
document.write( "Also from algebra, xz = 1.\r<BR>\n" );
document.write( "\n" );
document.write( "==> z = 1/x.\r<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+%2B+1%2Fx+=+1%2Fx+%2B+1%2Fx+=+2%2Fx+%3C%3E1+ ALIGN=MIDDLE  ALT=\"z+%2B+1%2Fx+=+1%2Fx+%2B+1%2Fx+=+2%2Fx+%3C%3E1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since 2/x would be a (non-real) complex number. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );