document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1000717>Question 1000717</A>: <I><SPAN STYLE=\"word-break: break-all;\"> e^(x)+e^(-x)=3<BR>\n" );
document.write( "x=0.9624 and -0.9624 but please explain how to get there.<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618090 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618090\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> e^(x)+e^(-x)=3<BR>\n" );
document.write( "x=0.9624 and -0.9624 but please explain how to get there.<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "e^(x)+e^(-x)=3<BR>\n" );
document.write( "Multiply thru by e^x<BR>\n" );
document.write( "e^(2x)+ 1 = 3e^x<BR>\n" );
document.write( "e^2x - 3e^x + 1 = 0<BR>\n" );
document.write( "Sub u for e^x<BR>\n" );
document.write( "u^2 - 3u + 1 = 0<BR>\n" );
document.write( "Solve for u.<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "e^x = u<BR>\n" );
document.write( "x = ln(u)<BR>\n" );
document.write( "========================<BR>\n" );
document.write( "As the other tutor mentioned, this is the hyperbolic cosine.<BR>\n" );
document.write( "The hyperbolic sine is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5E%28x%29-e%5E%28-x%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28e%5E%28x%29-e%5E%28-x%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );