document.write( "Question 828264: Solve :
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Algebra.Com's Answer #499243 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "y³ - 9x² + 27x - 27 = 0\r\n" );
document.write( "z³ - 9y² + 27y - 27 = 0\r\n" );
document.write( "x³ - 9z² + 27z - 27 = 0\r\n" );
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document.write( "Since all the equations will be the same if x = y = z,\r\n" );
document.write( "that must give a solution:\r\n" );
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document.write( "x³ - 9x² + 27x - 27 = 0\r\n" );
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document.write( "Possible zeros are ±1, ±3, ±9, ±27\r\n" );
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document.write( "We find that when we try x = 3\r\n" );
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document.write( "3 | 1  -9  27  -27\r\n" );
document.write( "  |     3 -18   27\r\n" );
document.write( "    1  -6   9    0\r\n" );
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document.write( "we can factor it as\r\n" );
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document.write( "(x - 3)(x² - 6x + 9) = 0\r\n" );
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document.write( "and factor it further as\r\n" );
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document.write( "(x - 3)(x - 3)(x - 3) = 0\r\n" );
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document.write( "             (x - 3)³ = 0\r\n" );
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document.write( "                x - 3 = 0\r\n" );
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document.write( "                    x = 3\r\n" );
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document.write( "Thus x=3, y=3, z=3 is a solution.  \r\n" );
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document.write( "There are 5 complex solutions as well:\r\n" );
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document.write( "x=-9.97528-0.398972i, y=-5.51359+9.06114i, z=0.872034+10.5311i\r\n" );
document.write( "x=-9.97528+0.398972i, y=-5.51359-9.06114i, z=0.872034-10.5311i\r\n" );
document.write( "x=-8.0106-5.47326i, y=9.67166+3.49043i, z-6.35574+6.29188i\r\n" );
document.write( "x=-8.0106+5.47326i, y=9.67166-3.49043i, z=-6.35574-6.29188i\r\n" );
document.write( "x=-6.35574-6.29188i, y=-8.0106+5.47326i, z=9.67166-3.49043i\r\n" );
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document.write( "but I think finding those is beyond the scope of your course.\r\n" );
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document.write( "Edwin
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