document.write( "Question 769183: Find all the zeroes of x cubed-3 ?
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Algebra.Com's Answer #468754 by Edwin McCravy(20081) $\"\"$ $\"About$

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document.write( "x³ - 3 = 0\r\n" );
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document.write( "    x³ = 3\r\n" );
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document.write( "So the zeros are the 3 cube roots of 3\r\n" );
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document.write( "3 = 3[cos(2pn) + i·sin(2pn)]\r\n" );
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document.write( "To get the three cube roots of 3, we use DeMoivre's theorem\r\n" );
document.write( "using the power of \r\n" );
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document.write( "∛3[cos + i·sin]\r\n" );
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document.write( "To get the first cube root, we let n=0\r\n" );
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document.write( "∛3[cos + i·sin] = ∛3[cos(0) + i·sin(0)] = ∛3[1 + 0i] = ∛3\r\n" );
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document.write( "To get the second cube root of 3, we let n=1\r\n" );
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document.write( "∛3[cos + i·sin] = ∛3[cos + i·sin] = ∛3[ + i·] =\r\n" );
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document.write( "and we can write \r\n" );
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document.write( "So the second cube root of 3 is \r\n" );
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document.write( "To get the third cube root of 3, we let n=2\r\n" );
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document.write( "∛3[cos + i·sin] = ∛3[cos + i·sin]\r\n" );
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document.write( "and since cos = cos, and sin = -sin,\r\n" );
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document.write( "the third cube root is just the conjugate of the \r\n" );
document.write( "second cube root, or\r\n" );
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document.write( "So the zeros of x³ - 3 are:\r\n" );
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document.write( "∛3, , and \r\n" );
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document.write( "Edwin

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