document.write( "Question 1209645: Find all complex solutions to the equation z^8 + 16 = 17z^4 - 8z^6 - 8z^2.
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Algebra.Com's Answer #849739 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "In the post by @CPhill, there is a serious deception of the reader.\r
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document.write( "Indeed, in his post, @CPhill reduced the original equation to the form\r\n" );
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document.write( "   u⁴ + 8u³ - 17u² + 8u + 16 = 0.\r\n" );
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document.write( "Till this point, everything is correct.\r\n" );
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document.write( "But then he writes\r\n" );
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document.write( "4. **Try factoring by grouping or other methods:**\r\n" );
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document.write( "This quartic equation is still not easily factored. But we should notice something interesting: the coefficients are symmetric (1, 8, -17, 8, 1). \r\n" );
document.write( "This suggests that we should try to divide both sides by u².\r\n" );
document.write( "u² + 8u - 17 + 8/u + 1/u² = 0\r\n" );
document.write( "(u² + 1/u²) + 8(u + 1/u) - 17 = 0\r\n" );
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document.write( "and continues further.\r\n" );
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document.write( "        But the coefficients  ARE NOT  (1, 8, -17, 8, 1).\r\n" );
document.write( "        They are                       (1, 8, -17, 8, 16),  and  THERE IS NO   symmetry.\r\n" );
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document.write( "So, this method does not work, and everything which follows in the post by @CPhill is not relevant to the given problem.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is WHY I call it \"a serious deception of the reader.\"\r
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