SOLUTION: Hopefully someone can point out where i am going wrong: {{{x^6-9x^3+8=0}}} -- I let U = x^3 -- {{{U^2 -9U +8 = 0}}} -- {{{U^2-9U+(81/4) = (49/4)}}} -- {{{(2U-9)^2/4 = 49

Question 560674: Hopefully someone can point out where i am going wrong:

--
I let U = x^3
--

--

--

--
= +/-
--
U = 1, 8
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Sub x^3 back for U
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x=1
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x=2
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Problem is the book shows the answer to be:
+/-

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The mistake occurred when you had x^3 = 1 and x^3 = 8 and concluded that the roots were 1 and 2. However x^3 = 1 has three roots of unity in the complex plane, namely

The roots for x^3 = 8 are similar, except twice as much (e.g. each root of x^3 = 1, multiplied by 2).
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