document.write( "Question 508704: if the product of two numbers is 21 and the sum is 10, what are the two numbers \n" ); document.write( "
Algebra.Com's Answer #341072 by Edwin McCravy(20060)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "\r\n" ); document.write( "The funny thing about this problem is, that in order\r\n" ); document.write( "to factor the binomial that results, you have think\r\n" ); document.write( "of two numbers whose product is 21 and whose sum is 10,\r\n" ); document.write( "which means you have to solve the problem in order to\r\n" ); document.write( "solve it!!!!\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( " (x-3)(x-7) = 0\r\n" ); document.write( " \r\n" ); document.write( "\r\n" ); document.write( " xy = 21\r\n" ); document.write( " x+y = 10\r\n" ); document.write( "\r\n" ); document.write( "Solve the second equation for y\r\n" ); document.write( "\r\n" ); document.write( " x+y = 10\r\n" ); document.write( " y = 10-x\r\n" ); document.write( "\r\n" ); document.write( "Substitute 10-x for y in\r\n" ); document.write( "\r\n" ); document.write( " xy = 21\r\n" ); document.write( " x(10-x) = 21 \r\n" ); document.write( " 10x-x² = 21\r\n" ); document.write( " -x²+10x-21 = 0\r\n" ); document.write( "\r\n" ); document.write( "Multiply through by -1\r\n" ); document.write( "\r\n" ); document.write( " x²-10x+21 = 0\r\n" ); document.write( " (x-3)(x-7) = 0 <--- here is where you have to know the solution\r\n" ); document.write( " to the problem already in order to do this factoring!!!\r\n" ); document.write( "x-3 = 0 x-7 = 0\r\n" ); document.write( " x = 3 x = 7 \r\n" ); document.write( "\r\n" ); document.write( "Substituting each in y = 10-x\r\n" ); document.write( "\r\n" ); document.write( "y = 10-3 y = 10-7 \r\n" ); document.write( "y = 7 x = 3\r\n" ); document.write( "\r\n" ); document.write( "It looks like there's two solutions but\r\n" ); document.write( "it's really only one pair of numbers, {3,7}\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |