r^4-k^4=0

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

Simplifying
r4 + -1k4 = 0

Reorder the terms:
-1k4 + r4 = 0

Solving
-1k4 + r4 = 0

Solving for variable 'k'.

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

Add '-1r4' to each side of the equation.
-1k4 + r4 + -1r4 = 0 + -1r4

Combine like terms: r4 + -1r4 = 0
-1k4 + 0 = 0 + -1r4
-1k4 = 0 + -1r4
Remove the zero:
-1k4 = -1r4

Divide each side by '-1'.
k4 = r4

Simplifying
k4 = r4

Combine like terms: r4 + -1r4 = 0
k4 + -1r4 = 0

Factor a difference between two squares.
(k2 + r2)(k2 + -1r2) = 0

Factor a difference between two squares.
(k2 + r2)((k + r)(k + -1r)) = 0

Subproblem 1
Set the factor '(k2 + r2)' equal to zero and attempt to solve:

Simplifying
k2 + r2 = 0

Solving
k2 + r2 = 0

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

Add '-1r2' to each side of the equation.
k2 + r2 + -1r2 = 0 + -1r2

Combine like terms: r2 + -1r2 = 0
k2 + 0 = 0 + -1r2
k2 = 0 + -1r2
Remove the zero:
k2 = -1r2

Simplifying
k2 = -1r2

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 + r)' equal to zero and attempt to solve:

Simplifying
k + r = 0

Solving
k + r = 0

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

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

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

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

Simplifying
k + -1r = 0

Solving
k + -1r = 0

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

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

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

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