document.write( "Question 1081841: The sum of the reciprocal of two numbers is 5. The product of the reciprocal of the two
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Algebra.Com's Answer #695887 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x and y be the two numbers under the question.\r\n" );
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document.write( "Then their reciprocals are  and , and the condition says\r\n" );
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document.write( " = 5,        (1)\r\n" );
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document.write( " = 18.   (2)\r\n" );
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document.write( "The last equation is equivalent to\r\n" );
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document.write( " = 6.      (3)\r\n" );
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document.write( "So, you need to solve the system (1),(3).\r\n" );
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document.write( "To make it easier, introduce new variables  a = , b = .\r\n" );
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document.write( "Then the system (1),(3) takes the form\r\n" );
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document.write( "a + b = 5,     (4)\r\n" );
document.write( "ab    = 6.     (5)\r\n" );
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document.write( "From (4),  a = 5-b.  Substitute it into (4). You will get\r\n" );
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document.write( "(5-b)*b = 6,\r\n" );
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document.write( "5b - b^2 = 6,\r\n" );
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document.write( "b^2 - 5b + 6 = 0,\r\n" );
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document.write( "(b-2)*(b-3) = 0.\r\n" );
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document.write( "The roots are  = 2   and   = 3.\r\n" );
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document.write( "1.  If  b = 2, then a = 3,  and x = ,  y = .\r\n" );
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document.write( "2.  If  b = 3, then a = 2,  and x = ,  y = .\r\n" );
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document.write( "Answer.  The two numbers are    and  .\r\n" );
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