document.write( "Question 1103636: the sum of the squares of two numbers is 72. The product of the two numbers is 36. Find the two numbers. \n" ); document.write( "

Algebra.Com's Answer #718349 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "x^2 + y^2 = 72,    (1)\r\n" );
document.write( "xy        = 36.    (2)\r\n" );
document.write( "\r\n" );
document.write( "====================>\r\n" );
document.write( "\r\n" );
document.write( "x^2 - 2xy + y^2 = 72 - 2*36 = 0  ====>\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(x-y)^2 = 0  ====>  x = y  ====>\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then from (2)  x*x = 36   ====>  x^2 = 36  ====>  x = +/- 6.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The solutions are  (x,y) = (6,6)   and/or   (x,y) = (-6,-6).\r\n" );
document.write( "

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

\n" );