document.write( "Question 893165: Seperate 30 into parts so that the sum of their squares is a minimum \n" ); document.write( "

Algebra.Com's Answer #541135 by josgarithmetic(39618) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%2By=30\"$ and interest in the expression $\"x%5E2%2By%5E2\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=30-x\"$ .
\n" ); document.write( " $\"y%5E2=%2830-x%29%5E2\"$
\n" ); document.write( " $\"900-30x-30x%2Bx%5E2\"$
\n" ); document.write( " $\"900-60x%2Bx%5E2\"$
\n" ); document.write( "-
\n" ); document.write( "-
\n" ); document.write( "The sum of squares expression is
\n" ); document.write( " $\"x%5E2%2B%28x%5E2-60x%2B900%29\"$
\n" ); document.write( " $\"2x%5E2-60x%2B900\"$ -------This does have a minimum.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2%28x%5E2-15x%2B450%29\"$
\n" ); document.write( " $\"highlight%282%28x%2B15%29%28x-30%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( "The roots are -15 and 30.
\n" ); document.write( "The minimum value of $\"2%28x%2B15%29%28x-30%29\"$ will occur in the exact middle of these roots.
\n" ); document.write( "-
\n" ); document.write( " $\"%28-15%2B30%29%2F2=15%2F2=7%261%2F2\"$ , for x.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The minimum value for the sum of those squares will be for $\"highlight%28x=15%2F2%29\"$ and $\"highlight%28y=30-7%261%2F2=22%261%2F2%29\"$ . \n" ); document.write( "

\n" );