document.write( "Question 447475: the sum of two number is 8, and the sum of their squares is 34. what is the smaller number \n" ); document.write( "

Algebra.Com's Answer #308052 by Edwin McCravy(20056) $\"\"$ $\"About$

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the sum of two number is 8, and the sum of their squares is 34. what is the smaller number
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document.write( "                x + y  =  8\r\n" );
document.write( "               x² + y² = 34\r\n" );
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document.write( "Solve the first equation for y\r\n" );
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document.write( "                     y = 8 - x\r\n" );
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document.write( "Substitute (8 - x) for y in the second equation:\r\n" );
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document.write( "         x² + (8 - x)² = 34 \r\n" );
document.write( "   x² + (8 - x)(8 - x) = 34\r\n" );
document.write( "x² + 64 - 8x - 8x + x² = 34\r\n" );
document.write( "        2x² + 64 - 16x = 34\r\n" );
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document.write( "Get 0 on the right:\r\n" );
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document.write( "        2x² + 30 - 16x = 0\r\n" );
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document.write( "Attange in order of descending powers \r\n" );
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document.write( "        2x² - 16x + 30 = 0\r\n" );
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document.write( "Divide every term by 2\r\n" );
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document.write( "          x² - 8x + 15 = 0\r\n" );
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document.write( "Factor the left side:\r\n" );
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document.write( "        (x - 5)(x - 3) = 0\r\n" );
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document.write( "Use the zero-factor principle:\r\n" );
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document.write( "x - 5 = 0;     x - 3 = 0\r\n" );
document.write( "    x = 5;         x = 3\r\n" );
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document.write( "We must find the corresponding value of y for\r\n" );
document.write( "each of these solutions for x:\r\n" );
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document.write( "for x = 5, substitute in\r\n" );
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document.write( "                     y = 8 - x\r\n" );
document.write( "                     y = 8 - 5\r\n" );
document.write( "                     y = 3\r\n" );
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document.write( "So one solution is (x,y) = (5,3)\r\n" );
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document.write( "for x = 3, substitute in\r\n" );
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document.write( "                     y = 8 - x\r\n" );
document.write( "                     y = 8 - 3\r\n" );
document.write( "                     y = 5\r\n" );
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document.write( "So the other solution is (x,y) = (3,5)\r\n" );
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document.write( "The question asked for the smaller number, which is 3.\r\n" );
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document.write( "FYI, the graphical representation of the system is below\r\n" );
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document.write( "The equation x² + y² = 34 has a graph which is a circle, \r\n" );
document.write( "and x + y = 8 has a graph which is a straight line and \r\n" );
document.write( "the line cuts the circle in two points (3,5) and (5,3), \r\n" );
document.write( "as you see below:\r\n" );
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document.write( "Edwin

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