Question 1209645
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Find all complex solutions to the equation z^8 + 16 = 17z^4 - 8z^6 - 8z^2.
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In the post by @CPhill, there is a serious deception of the reader.


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Indeed, in his post, @CPhill reduced the original equation to the form

   u⁴ + 8u³ - 17u² + 8u + 16 = 0.


Till this point, everything is correct.



But then he writes

4. **Try factoring by grouping or other methods:**

This quartic equation is still not easily factored. But we should notice something interesting: the coefficients are symmetric (1, 8, -17, 8, 1). 
This suggests that we should try to divide both sides by u².
u² + 8u - 17 + 8/u + 1/u² = 0
(u² + 1/u²) + 8(u + 1/u) - 17 = 0


and continues further.


        But the coefficients  ARE NOT  (1, 8, -17, 8, 1).
        They are                       (1, 8, -17, 8, 16),  and  THERE IS NO   symmetry.


So, this method does not work, and everything which follows in the post by @CPhill is not relevant to the given problem.
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It is WHY I call it "a serious deception of the reader."