document.write( "Question 868394: I have no idea how to solve this and my book has no examples to show me. \"What is the minimum product of two numbers whose difference is 4?\" \n" ); document.write( "

Algebra.Com's Answer #523517 by Edwin McCravy(20065) $\"\"$ $\"About$

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I have no idea how to solve this and my book has no examples to show me. \"What is the minimum product of two numbers whose difference is 4?\"
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document.write( "Let z = one number\r\n" );
document.write( "Let x = other number\r\n" );
document.write( "Let y = their product = xz\r\n" );
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document.write( "So y = xz\r\n" );
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document.write( "Since their difference is 4\r\n" );
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document.write( "z - x = 4\r\n" );
document.write( "    z = 4+x\r\n" );
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document.write( "   y = xz\r\n" );
document.write( "   y = x(4+x)\r\n" );
document.write( "   y = 4x+x²\r\n" );
document.write( "   y = x²+4x\r\n" );
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document.write( "This is a parabola that opens upward:\r\n" );
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document.write( "   \r\n" );
document.write( "So its lowest point is the minimum value of y.  That is the vertex.\r\n" );
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document.write( "The x-coordinate of the vertex is  =  = -2\r\n" );
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document.write( "Its y-coordinate is found by substituting x = -2 in\r\n" );
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document.write( "   y = x²+4x\r\n" );
document.write( "   y = (-2)²+4(-2)\r\n" );
document.write( "   y = 4-8\r\n" );
document.write( "   y = -4\r\n" );
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document.write( "So the vertex is (-2,-4)\r\n" );
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document.write( "Since y = the product, the minimum product is -4.\r\n" );
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document.write( "Edwin

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