v^5=v^3

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Solution for v^5=v^3 equation:


Simplifying
v5 = v3

Solving
v5 = v3

Solving for variable 'v'.

Reorder the terms:
-1v3 + v5 = v3 + -1v3

Combine like terms: v3 + -1v3 = 0
-1v3 + v5 = 0

Factor out the Greatest Common Factor (GCF), 'v3'.
v3(-1 + v2) = 0

Factor a difference between two squares.
v3((1 + v)(-1 + v)) = 0

Subproblem 1

Set the factor 'v3' equal to zero and attempt to solve: Simplifying v3 = 0 Solving v3 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v3 = 0 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 + v)' equal to zero and attempt to solve: Simplifying 1 + v = 0 Solving 1 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + v = 0 + -1 v = 0 + -1 Combine like terms: 0 + -1 = -1 v = -1 Simplifying v = -1

Subproblem 3

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

Solution

v = {-1, 1}

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