document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175883>Question 1175883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let x, y, and z be nonzero real numbers, such that no two are equal, and<BR>\n" );
document.write( "x + {1}/{y} = y + {1}/{z} = z + {1}/{x}. Find all possible numeric values of xyz. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801622 by </B><A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><B>CubeyThePenguin(3113)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><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=CubeyThePenguin><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=801622\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x + 1/y = y + 1/z = z + 1/x\r<BR>\n" );
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document.write( "We have a system of three equations:\r<BR>\n" );
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document.write( "x + 1/y = y + 1/z<BR>\n" );
document.write( "x + 1/y = z + 1/x<BR>\n" );
document.write( "y + 1/z = z + 1/x\r<BR>\n" );
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document.write( "Solving, we get (x, y, z) = (-1, 1/2, 2) or (1, -1/2, -2). The product xyz can be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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