a^5=a^3

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Solution for a^5=a^3 equation:


Simplifying
a5 = a3

Solving
a5 = a3

Solving for variable 'a'.

Reorder the terms:
-1a3 + a5 = a3 + -1a3

Combine like terms: a3 + -1a3 = 0
-1a3 + a5 = 0

Factor out the Greatest Common Factor (GCF), 'a3'.
a3(-1 + a2) = 0

Factor a difference between two squares.
a3((1 + a)(-1 + a)) = 0

Subproblem 1

Set the factor 'a3' equal to zero and attempt to solve: Simplifying a3 = 0 Solving a3 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a3 = 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 + a)' equal to zero and attempt to solve: Simplifying 1 + a = 0 Solving 1 + a = 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 + a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0 + -1 a = 0 + -1 Combine like terms: 0 + -1 = -1 a = -1 Simplifying a = -1

Subproblem 3

Set the factor '(-1 + a)' equal to zero and attempt to solve: Simplifying -1 + a = 0 Solving -1 + a = 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 + a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + a = 0 + 1 a = 0 + 1 Combine like terms: 0 + 1 = 1 a = 1 Simplifying a = 1

Solution

a = {-1, 1}

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