document.write( "Question 358617: the sum of two numbers is the same as their product, and the difference of thier reciprocals is 3. find the numbers \n" ); document.write( "

Algebra.Com's Answer #255963 by Edwin McCravy(20056) $\"\"$ $\"About$

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the sum of two numbers is the same as their product, and the difference of thier recoprocals is 3. find the numbers
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document.write( "Let the numbers be x and y\r\n" );
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document.write( "The sum of the the numbers = x + y\r\n" );
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document.write( "The product of the numbers = xy\r\n" );
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document.write( "The reciprocal of x is \r\n" );
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document.write( "The reciprocal of y is \r\n" );
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document.write( "\"the sum of two numbers x+y is the same as their product xy\",\r\n" );
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document.write( "so  \r\n" );
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document.write( "\"the difference of their recoprocals  is 3\",\r\n" );
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document.write( "so  \r\n" );
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document.write( "So we have the system of equations \r\n" );
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document.write( "Clear the second equation of fractions by multiplying through by LCD xy\r\n" );
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document.write( "So the system  of equations is now\r\n" );
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document.write( "Write the left side of the first equation in reverse order:\r\n" );
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document.write( "Adding the two equations term by term,\r\n" );
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document.write( "2y = 4xy\r\n" );
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document.write( "Get 0 on the right side:\r\n" );
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document.write( "2y - 4xy = 0\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "y - 2xy = 0\r\n" );
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document.write( "y(1 - 2x) = 0\r\n" );
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document.write( "Set each factor = 0\r\n" );
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document.write( "y = 0;   1 - 2x = 0\r\n" );
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document.write( "            -2x = -1\r\n" );
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document.write( "              x = \r\n" );
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document.write( "y = 0 must be discarded because the reciprocal of 0 is not defined.\r\n" );
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document.write( "So x =   \r\n" );
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document.write( "Substituting in \r\n" );
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document.write( "Multiplying through by LCD of 2\r\n" );
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document.write( "1 + 2y = y\r\n" );
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document.write( "     y = -1\r\n" );
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document.write( "So the numbers are  and \r\n" );
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document.write( "Checking:\r\n" );
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document.write( "The sum of the the numbers = \r\n" );
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document.write( "The product of the numbers = \r\n" );
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document.write( "That checks because they are both the same.\r\n" );
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document.write( "The reciprocal of  is 2\r\n" );
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document.write( "The reciprocal of -1 is  or -1.\r\n" );
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document.write( "The difference of these reciprocals is \r\n" );
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document.write( "So that checks.\r\n" );
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document.write( "Edwin

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