document.write( "Question 1121449: a) Find the value of xyz, given that xy = 117, yz = 286 and xz = 198.
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Algebra.Com's Answer #737345 by ikleyn(52903) $\"\"$ $\"About$

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document.write( "You are given\r\n" );
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document.write( "    xy = 117     (1)\r\n" );
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document.write( "    yz = 286     (2)\r\n" );
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document.write( "    xz = 198     (3)\r\n" );
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document.write( "Multiply all 3 equations (1), (2) and (3) (both sides). You will get\r\n" );
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document.write( "    (xyz)^2 = 117*286*198 = 6625476;   hence,\r\n" );
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document.write( "    xyz = +/-  = +/- 2574.       (4)\r\n" );
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document.write( "First, consider the case  xyz = 2574      (5)\r\n" );
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document.write( "Divide equation (4) by equation (1).  You will get  z =  = 22.\r\n" );
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document.write( "Next divide equation (4) by equation (2).  You will get  x =  = 9.\r\n" );
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document.write( "Finally, divide equation (4) by equation (3).  You will get  y =  = 13.\r\n" );
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document.write( "Thus, in this case the solution is  (x,y,z) = (9,13,22).\r\n" );
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document.write( "Next consider the case   xyz = -2574.\r\n" );
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document.write( "Do the same operations, and you will get the second solution  (x,y,z) = (-9,-13,-22).\r\n" );
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document.write( "Answer.  The problem has two solutions  (x,y,z) = (9,13,22)  and  (x,y,z) = (-9,-13,-22).\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a classic problem and its standard/canonical solution.\r
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\n" ); document.write( "\n" ); document.write( "To see other similar problems solved in this way, look into the lesson\r
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