document.write( "Question 955351: Find the greatest value of \"xy\".
\n" ); document.write( "If ( (a^2 x^4) + ( b^2 y^4) ) = c^6. ? \n" ); document.write( "

Algebra.Com's Answer #583583 by Fombitz(32388) $\"\"$ $\"About$

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$\"a%5E2+x%5E4+%2B+b%5E2+y%5E4+=+c%5E6\"$
\n" ); document.write( " $\"b%5E2y%5E4=c%5E6-a%5E2x%5E4\"$
\n" ); document.write( " $\"y%5E4=%28c%5E6-a%5E2x%5E4%29%2Fb%5E2\"$
\n" ); document.write( " $\"y=%28%28c%5E6-a%5E2x%5E4%29%2Fb%5E2%29%5E%281%2F4%29\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"Z=xy\"$
\n" ); document.write( " $\"Z=x%28%28c%5E6-a%5E2x%5E4%29%2Fb%5E2%29%5E%281%2F4%29\"$
\n" ); document.write( "Taking the derivative of Z with respect to x,
\n" ); document.write( "

\n" ); document.write( "To find the extrema, set the derivative equal to zero.
\n" ); document.write( " $\"c%5E6-2a%5E2x%5E4=0\"$
\n" ); document.write( " $\"2a%5E2x%5E4=c%5E6\"$
\n" ); document.write( " $\"x%5E4=c%5E6%2F%282a%5E2%29\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"a%5E2%28c%5E6%2F%282a%5E2%29%29%2Bb%5E2y%5E4=c%5E6\"$
\n" ); document.write( " $\"c%5E6%2F2%2Bb%5E2y%5E4=c%5E6\"$
\n" ); document.write( " $\"b%5E2y%5E4=c%5E6%2F2\"$ }
\n" ); document.write( " $\"y%5E4=c%5E6%2F%282b%5E2%29\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"x%5E4y%5E4=%28c%5E6%2F%282a%5E2%29%29%28c%5E6%2F%282b%5E2%29%29\"$
\n" ); document.write( " $\"%28xy%29%5E4=c%5E12%2F%284a%5E2b%5E2%29\"$
\n" ); document.write( "and finally,
\n" ); document.write( " $\"xy%5Bmax%5D=%28c%5E12%5E%281%2F4%29%29%2F%284a%5E2b%5E2%29%5E%281%2F4%29\"$
\n" ); document.write( " $\"highlight%28xy%5Bmax%5D=c%5E3%2Fsqrt%282ab%29%29\"$
\n" ); document.write( " \n" ); document.write( "

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