a^6-2a^3+1=0

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Solution for a^6-2a^3+1=0 equation:


Simplifying
a6 + -2a3 + 1 = 0

Reorder the terms:
1 + -2a3 + a6 = 0

Solving
1 + -2a3 + a6 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + -1a3)(1 + -1a3) = 0

Subproblem 1

Set the factor '(1 + -1a3)' equal to zero and attempt to solve: Simplifying 1 + -1a3 = 0 Solving 1 + -1a3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a3 = 0 + -1 -1a3 = 0 + -1 Combine like terms: 0 + -1 = -1 -1a3 = -1 Divide each side by '-1'. a3 = 1 Simplifying a3 = 1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(1 + -1a3)' equal to zero and attempt to solve: Simplifying 1 + -1a3 = 0 Solving 1 + -1a3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1a3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a3 = 0 + -1 -1a3 = 0 + -1 Combine like terms: 0 + -1 = -1 -1a3 = -1 Divide each side by '-1'. a3 = 1 Simplifying a3 = 1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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