81y^4-4x^4=0

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Solution for 81y^4-4x^4=0 equation: 


Simplifying
81y4 + -4x4 = 0

Reorder the terms:
-4x4 + 81y4 = 0

Solving
-4x4 + 81y4 = 0

Solving for variable 'x'.

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

Add '-81y4' to each side of the equation.
-4x4 + 81y4 + -81y4 = 0 + -81y4

Combine like terms: 81y4 + -81y4 = 0
-4x4 + 0 = 0 + -81y4
-4x4 = 0 + -81y4
Remove the zero:
-4x4 = -81y4

Divide each side by '-4'.
x4 = 20.25y4

Simplifying
x4 = 20.25y4

Combine like terms: 20.25y4 + -20.25y4 = 0.00
x4 + -20.25y4 = 0.00

Factor a difference between two squares.
(x2 + 4.5y2)(x2 + -4.5y2) = 0.00


Subproblem 1
Set the factor '(x2 + 4.5y2)' equal to zero and attempt to solve:

Simplifying
x2 + 4.5y2 = 0

Solving
x2 + 4.5y2 = 0

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

Add '-4.5y2' to each side of the equation.
x2 + 4.5y2 + -4.5y2 = 0 + -4.5y2

Combine like terms: 4.5y2 + -4.5y2 = 0.0
x2 + 0.0 = 0 + -4.5y2
x2 = 0 + -4.5y2
Remove the zero:
x2 = -4.5y2

Simplifying
x2 = -4.5y2

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 '(x2 + -4.5y2)' equal to zero and attempt to solve:

Simplifying
x2 + -4.5y2 = 0

Solving
x2 + -4.5y2 = 0

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

Add '4.5y2' to each side of the equation.
x2 + -4.5y2 + 4.5y2 = 0 + 4.5y2

Combine like terms: -4.5y2 + 4.5y2 = 0.0
x2 + 0.0 = 0 + 4.5y2
x2 = 0 + 4.5y2
Remove the zero:
x2 = 4.5y2

Simplifying
x2 = 4.5y2

Take the square root of each side:
x = {-2.121320344y, 2.121320344y}
Solution
x = {-2.121320344y, 2.121320344y}

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