document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977299>Question 977299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x and y are two positive real nos. such that their sum is 1, then find the maximum value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%5E4+%2B+yx%5E4 ALIGN=MIDDLE  ALT=\"xy%5E4+%2B+yx%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(Please solve using basic algebra and logic and NOT using calculus) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #598846 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=598846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x+y=1<BR>\n" );
document.write( "y=1-x<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%281-x%29%5E4%2B%281-x%29x%5E4 ALIGN=MIDDLE  ALT=\"x%281-x%29%5E4%2B%281-x%29x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%281-x%29%28%281-x%29%5E3%2Bx%5E3%29 ALIGN=MIDDLE  ALT=\"x%281-x%29%28%281-x%29%5E3%2Bx%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%281-x%29%28-x%5E3-x%5E2-3x%2B1%2Bx%5E2%29 ALIGN=MIDDLE  ALT=\"x%281-x%29%28-x%5E3-x%5E2-3x%2B1%2Bx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%281-x%29%28-x%5E2-3x%2B1%29 ALIGN=MIDDLE  ALT=\"x%281-x%29%28-x%5E2-3x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29x%281-x%29%28x%5E2%2B3x-1%29 ALIGN=MIDDLE  ALT=\"%28-1%29x%281-x%29%28x%5E2%2B3x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You may be able to identify roots of the factored expression and on which intervals is the expression positive.  You could check using iterations of numerical values to find max values as near as you want for any maximum values which exist.\r<BR>\n" );
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document.write( "The ROOTS  (not any extremes)  are  0, 1, (-3-sqrt(13))/2, (-3+sqrt(13))/2.<BR>\n" );
document.write( "Remember you wanted positive values for x, and that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3Cx%3C1 ALIGN=MIDDLE  ALT=\"0%3Cx%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "I have not worked through to any finished answer; just planned for the method. </SPAN>\n" );
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