document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=474645>Question 474645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let x and y be nonzero, real numbers such that -1 < x < 1 and -2 < y < 2. Suppose x/y + y/x = z, where z is some real number. Which of the following is true for all possible z? choose the answer and explain the reason to choose your response<BR>\n" );
document.write( " z is less than 10^k for some k>1 <BR>\n" );
document.write( "z is positive<BR>\n" );
document.write( " xyz can be negative <BR>\n" );
document.write( "The other three answers are false </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #325518 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=325518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE z = \frac{x}{y} + \frac{y}{x} = \frac{x^2 + y^2}{xy}\">.\r<BR>\n" );
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document.write( "The first choice \"z is less than 10^k for some k>1\" is not necessarily true (even if we let k get really large) because z can also go to infinity.\r<BR>\n" );
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document.write( "z does not have to be positive (e.g. let x and y have different signs).\r<BR>\n" );
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document.write( "xyz can be negative, but xyz can also be positive (let x,y be positive).\r<BR>\n" );
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document.write( "Hence, the last choice \"the other three answers are false\" is correct because the first three choices have counterexamples; i.e. the statements are not true for all possible z. </SPAN>\n" );
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