k^8-2k^4=-1

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Solution for k^8-2k^4=-1 equation:


Simplifying
k8 + -2k4 = -1

Reorder the terms:
-2k4 + k8 = -1

Solving
-2k4 + k8 = -1

Solving for variable 'k'.

Reorder the terms:
1 + -2k4 + k8 = -1 + 1

Combine like terms: -1 + 1 = 0
1 + -2k4 + k8 = 0

Factor a trinomial.
(1 + -1k4)(1 + -1k4) = 0

Factor a difference between two squares.
((1 + k2)(1 + -1k2))(1 + -1k4) = 0

Factor a difference between two squares.
((1 + k2)((1 + k)(1 + -1k)))(1 + -1k4) = 0

Factor a difference between two squares.
((1 + k2)(1 + -1k2))(1 + k2)(1 + k)(1 + -1k) = 0

Factor a difference between two squares.
((1 + k2)((1 + k)(1 + -1k)))(1 + k2)(1 + k)(1 + -1k) = 0

Subproblem 1

Set the factor '(1 + k2)' equal to zero and attempt to solve: Simplifying 1 + k2 = 0 Solving 1 + k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k2 = 0 + -1 k2 = 0 + -1 Combine like terms: 0 + -1 = -1 k2 = -1 Simplifying k2 = -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 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1

Subproblem 3

Set the factor '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1

Subproblem 4

Set the factor '(1 + k2)' equal to zero and attempt to solve: Simplifying 1 + k2 = 0 Solving 1 + k2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k2 = 0 + -1 k2 = 0 + -1 Combine like terms: 0 + -1 = -1 k2 = -1 Simplifying k2 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 5

Set the factor '(1 + k)' equal to zero and attempt to solve: Simplifying 1 + k = 0 Solving 1 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + k = 0 + -1 k = 0 + -1 Combine like terms: 0 + -1 = -1 k = -1 Simplifying k = -1

Subproblem 6

Set the factor '(1 + -1k)' equal to zero and attempt to solve: Simplifying 1 + -1k = 0 Solving 1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1k = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1k = 0 + -1 -1k = 0 + -1 Combine like terms: 0 + -1 = -1 -1k = -1 Divide each side by '-1'. k = 1 Simplifying k = 1

Solution

k = {-1, 1, -1, 1}

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