p^4-k^4=0

Solution for p^4-k^4=0 equation:

Simplifying
p4 + -1k4 = 0

Reorder the terms:
-1k4 + p4 = 0

Solving
-1k4 + p4 = 0

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-1p4' to each side of the equation.
-1k4 + p4 + -1p4 = 0 + -1p4

Combine like terms: p4 + -1p4 = 0
-1k4 + 0 = 0 + -1p4
-1k4 = 0 + -1p4
Remove the zero:
-1k4 = -1p4

Divide each side by '-1'.
k4 = p4

Simplifying
k4 = p4

Combine like terms: p4 + -1p4 = 0
k4 + -1p4 = 0

Factor a difference between two squares.
(k2 + p2)(k2 + -1p2) = 0

Factor a difference between two squares.
(k2 + p2)((k + p)(k + -1p)) = 0

Subproblem 1
Set the factor '(k2 + p2)' equal to zero and attempt to solve:

Simplifying
k2 + p2 = 0

Solving
k2 + p2 = 0

Move all terms containing k to the left, all other terms to the right.

Add '-1p2' to each side of the equation.
k2 + p2 + -1p2 = 0 + -1p2

Combine like terms: p2 + -1p2 = 0
k2 + 0 = 0 + -1p2
k2 = 0 + -1p2
Remove the zero:
k2 = -1p2

Simplifying
k2 = -1p2

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 '(k + p)' equal to zero and attempt to solve:

Simplifying
k + p = 0

Solving
k + p = 0

Move all terms containing k to the left, all other terms to the right.

Add '-1p' to each side of the equation.
k + p + -1p = 0 + -1p

Combine like terms: p + -1p = 0
k + 0 = 0 + -1p
k = 0 + -1p
Remove the zero:
k = -1p

Simplifying
k = -1p
Subproblem 3
Set the factor '(k + -1p)' equal to zero and attempt to solve:

Simplifying
k + -1p = 0

Solving
k + -1p = 0

Move all terms containing k to the left, all other terms to the right.

Add 'p' to each side of the equation.
k + -1p + p = 0 + p

Combine like terms: -1p + p = 0
k + 0 = 0 + p
k = 0 + p
Remove the zero:
k = p

Simplifying
k = p
Solution
k = {-1p, p}