document.write( "Question 596131: If x²+x+1=0, then what is the value of (x³+ $\"1%2Fx%5E3\"$ )³ ?
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Algebra.Com's Answer #377533 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "Notice that x²+x+1 one of the factors of x³-1 because\r\n" );
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document.write( "x³-1 = (x-1)(x²+x+1)\r\n" );
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document.write( "Then since x²+x+1 = 0, \r\n" );
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document.write( "x³-1 = (x-1)(x²+x+1) = (x-1)(0) = 0\r\n" );
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document.write( "and therefore\r\n" );
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document.write( " x³-1 = 0\r\n" );
document.write( "   x³ = 1 \r\n" );
document.write( "    x =  \r\n" );
document.write( "    x = 1\r\n" );
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document.write( "Therefore  (x³+)³ = (1³+)³ = (1+)³ = (1+1)³ = 2³ = 8\r\n" );
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document.write( "Edwin

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