document.write( "Question 977299: If x and y are two positive real nos. such that their sum is 1, then find the maximum value of $\"xy%5E4+%2B+yx%5E4\"$
\n" ); document.write( "(Please solve using basic algebra and logic and NOT using calculus) \n" ); document.write( "

Algebra.Com's Answer #598851 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
If x and y are two positive real nos. such that their sum is 1, then find the maximum value of $\"xy%5E4+%2B+yx%5E4\"$
\n" ); document.write( "(Please solve using basic algebra and logic and NOT using calculus)
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since x+y=1, substitute 1-x for y\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If we can find A, B and nonnegative C such that\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "then it's easy to see that z will have its maximum value \r\n" );
document.write( "when the quadratic  equals 0, and that maximum\r\n" );
document.write( "value will be C. \r\n" );
document.write( "\r\n" );
document.write( "Let's see if we can find such A, B, and C by equating\r\n" );
document.write( "coefficients:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Equating coefficients of x³:  , or \r\n" );
document.write( "\r\n" );
document.write( "Equating coefficients of x²:  \r\n" );
document.write( "                              \r\n" );
document.write( "                              \r\n" );
document.write( "                              \r\n" );
document.write( "                              \r\n" );
document.write( "                              \r\n" );
document.write( "\r\n" );
document.write( "Equating coefficients of x:  \r\n" );
document.write( "                             \r\n" );
document.write( "                               \r\n" );
document.write( "\r\n" );
document.write( "                              Already met.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Equating constant terms:      \r\n" );
document.write( "                              \r\n" );
document.write( "                              \r\n" );
document.write( "                              \r\n" );
document.write( "                              \r\n" );
document.write( "                              \r\n" );
document.write( "\r\n" );
document.write( "That's the answer \r\n" );
document.write( "\r\n" );
document.write( "z will take on that maximum value 1/12 when the quadratic \r\n" );
document.write( "takes on the value 0.  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply top and bottom by 3\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So there are two points where z reaches the maximum value of \r\n" );
document.write( "\r\n" );
document.write( "They are \r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );