x^4y^4=16

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Solution for x^4y^4=16 equation:


Simplifying
x4y4 = 16

Solving
x4y4 = 16

Solving for variable 'x'.

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

Divide each side by 'y4'.
x4 = 16y-4

Simplifying
x4 = 16y-4

Combine like terms: 16y-4 + -16y-4 = 0
x4 + -16y-4 = 0

Factor out the Greatest Common Factor (GCF), 'y-4'.
y-4(x4y4 + -16) = 0

Factor a difference between two squares.
y-4((x2y2 + 4)(x2y2 + -4)) = 0

Factor a difference between two squares.
y-4((x2y2 + 4)((xy + 2)(xy + -2))) = 0

Subproblem 1

Set the factor 'y-4' equal to zero and attempt to solve: Simplifying y-4 = 0 Solving y-4 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y-4' to each side of the equation. y-4 + -1y-4 = 0 + -1y-4 Remove the zero: 0 = -1y-4 Simplifying 0 = -1y-4 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 '(x2y2 + 4)' equal to zero and attempt to solve: Simplifying x2y2 + 4 = 0 Reorder the terms: 4 + x2y2 = 0 Solving 4 + x2y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x2y2 = 0 + -4 x2y2 = 0 + -4 Combine like terms: 0 + -4 = -4 x2y2 = -4 Divide each side by 'y2'. x2 = -4y-2 Simplifying x2 = -4y-2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(xy + 2)' equal to zero and attempt to solve: Simplifying xy + 2 = 0 Reorder the terms: 2 + xy = 0 Solving 2 + xy = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + xy = 0 + -2 Combine like terms: 2 + -2 = 0 0 + xy = 0 + -2 xy = 0 + -2 Combine like terms: 0 + -2 = -2 xy = -2 Divide each side by 'y'. x = -2y-1 Simplifying x = -2y-1

Subproblem 4

Set the factor '(xy + -2)' equal to zero and attempt to solve: Simplifying xy + -2 = 0 Reorder the terms: -2 + xy = 0 Solving -2 + xy = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + xy = 0 + 2 Combine like terms: -2 + 2 = 0 0 + xy = 0 + 2 xy = 0 + 2 Combine like terms: 0 + 2 = 2 xy = 2 Divide each side by 'y'. x = 2y-1 Simplifying x = 2y-1

Solution

x = {-2y-1, 2y-1}

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