document.write( "Question 1033415: Let x, y, and z be nonzero real numbers. Find all possible values of\r
\n" ); document.write( "\n" ); document.write( "(x)/(|x|) + (y)/(|y|) + (z)/(|z|) + (xyz)/(|xyz|).\r
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Algebra.Com's Answer #648019 by ikleyn(52795) $\"\"$ $\"About$

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\n" ); document.write( "Let x, y, and z be nonzero real numbers. Find all possible values of\r
\n" ); document.write( "\n" ); document.write( "(x)/(|x|) + (y)/(|y|) + (z)/(|z|) + (xyz)/(|xyz|).
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document.write( "Let F(x,y,z) =  +  +  + .\r\n" );
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document.write( "It is clear that it is sufficient to estimate/calculate F(x,y,z) at x = +/-1, y = +/-1 and z = +/-1. In total, there are 8 inputs.\r\n" );
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document.write( "If there are all \"+\" in the input, the result is 4.\r\n" );
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document.write( "If there is precisely 1 \"-\" in the input, then the result is 0.\r\n" );
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document.write( "If there are precisely 2 \"-\" in the input, then the result is 0.\r\n" );
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document.write( "If there are all \"-\" in the input, then the result is -4.\r\n" );
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document.write( "Answer. The list of all possible values is 4, 0, -4.\r\n" );
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