SOLUTION: Hopefully someone can point out where i am going wrong:
{{{x^6-9x^3+8=0}}}
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I let U = x^3
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{{{U^2 -9U +8 = 0}}}
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{{{U^2-9U+(81/4) = (49/4)}}}
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{{{(2U-9)^2/4 = 49
Question 560674: Hopefully someone can point out where i am going wrong:
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I let U = x^3
--
--
--
-- = +/-
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U = 1, 8
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Sub x^3 back for U
--- x=1
--- x=2
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Problem is the book shows the answer to be:
+/-
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).