document.write( "Question 775369: I'm having a hard time making an equation for this problem. Please explain how to solve this: The sum of the squares of two numbers is 18 and their product is 2. if their difference is 3, find the difference of their cubes. \n" ); document.write( "
Algebra.Com's Answer #472797 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
I'm having a hard time making an equation for this problem. Please explain how to solve this: The sum of the squares of two numbers is 18
\n" ); document.write( "
\r\n" );
document.write( "x2 + y2 = 18\r\n" );
document.write( "\r\n" );
document.write( "and their product is 2. \r\n" );
document.write( "\r\n" );
document.write( "xy = 2\r\n" );
document.write( "\r\n" );
document.write( "Solve the system:\r\n" );
document.write( "\r\n" );
document.write( "x2 + y2 = 18\r\n" );
document.write( "xy = 2\r\n" );
document.write( "\r\n" );
document.write( "Solve the second for y\r\n" );
document.write( "\r\n" );
document.write( "y = \"2%2Fx\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute in the first:\r\n" );
document.write( "\r\n" );
document.write( "x2 + \"%282%2Fx%29\"2 = 18\r\n" );
document.write( "\r\n" );
document.write( "x2 + \"%284%2Fx%5E2%29\" = 18\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by x2\r\n" );
document.write( "\r\n" );
document.write( "x4 + 4 = 18x²\r\n" );
document.write( "\r\n" );
document.write( "x4 - 18x2 + 4 = 0\r\n" );
document.write( "\r\n" );
document.write( "Solve that by the quadratic formula for x2\r\n" );
document.write( "and then take square roots you get\r\n" );
document.write( "\r\n" );
document.write( "one of them is approximately 4.216 and the other is \r\n" );
document.write( "approximately 0.474, or they could be the negatives of those.\r\n" );
document.write( "

\n" ); document.write( "if their difference is 3, find the difference of their cubes.
\n" ); document.write( "
\r\n" );
document.write( "Since their difference is not 3, the problem is botched.  You\r\n" );
document.write( "don't need to continue.  Point this error out to your teacher.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );