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)\"\" \"About 
You can put this solution on YOUR website!
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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" );
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document.write( "   (x-3)(x-7) = 0\r\n" );
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document.write( "        xy = 21\r\n" );
document.write( "       x+y = 10\r\n" );
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document.write( "Solve the second equation for y\r\n" );
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document.write( "       x+y = 10\r\n" );
document.write( "         y = 10-x\r\n" );
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document.write( "Substitute 10-x for y in\r\n" );
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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" );
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document.write( "Multiply through by -1\r\n" );
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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" );
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document.write( "Substituting each in y = 10-x\r\n" );
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document.write( "y = 10-3   y = 10-7  \r\n" );
document.write( "y = 7      x = 3\r\n" );
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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" );
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document.write( "Edwin
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