document.write( "Question 427410: If m + n = 3 and m^2 + n^2 = 6, find the exact value of m^3 + n^3. \n" ); document.write( "

Algebra.Com's Answer #297299 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
The expression $\"%28m+%2B+n%29%28m%5E2+%2B+n%5E2%29\"$ is equal to

.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Suppose we square both sides of $\"m+%2B+n+=+3\"$ to obtain $\"m%5E2+%2B+2mn+%2B+n%5E2+=+9\"$ . Replacing $\"m%5E2+%2B+n%5E2\"$ we get $\"6+%2B+2mn+=+9\"$ --> $\"mn+=+3%2F2\"$ . Replace $\"mn\"$ with $\"3%2F2\"$ in our first equation to get\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"m%5E3+%2B+n%5E3+%2B+3%283%2F2%29+=+18\"$ --> $\"m%5E3+%2B+n%5E3+=+18+-+9%2F2+=+27%2F2\"$ . \n" ); document.write( "

\n" );