document.write( "Question 1189711: Find the product of x•y, where x and y are positive integers and $\"+0=3x%5E4-x%5E3y-9317+\"$ \n" ); document.write( "

Algebra.Com's Answer #821149 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Find the product of x•y, where x and y are positive integers and $\"0+=+3x%5E4+-+x%5E3%2Ay-9317\"$ .
\n" ); document.write( "~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Given equation is equivalent to\r\n" );
document.write( "\r\n" );
document.write( "    3x^4 - x^3*y = 9317,  \r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "    x^3*(3x - y) = 9317.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Integer number 9317 has the primary decomposition  9317 = 7*11^3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From uniqueness of prime decomposition for integer numbers, we conclude that  \r\n" );
document.write( "\r\n" );
document.write( "    EITHER  x = 1,  3x-y = 9317  OR  x = 11 and  3*11 - y = 7;  y = 33-7 = 26.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "First option produces negative value of y; therefore, we discard it.\r\n" );
document.write( "\r\n" );
document.write( "The second option gives the ANSWER to the problem  x= 11, y = 26.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The requested product x*y = 11*26 = 286.    ANSWER\r\n" );
document.write( "

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

\n" );