x^4+x^2*y^2-2y^4=0

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Solution for x^4+x^2*y^2-2y^4=0 equation: 


Simplifying
x4 + x2 * y2 + -2y4 = 0

Multiply x2 * y2
x4 + x2y2 + -2y4 = 0

Reorder the terms:
x2y2 + x4 + -2y4 = 0

Solving
x2y2 + x4 + -2y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(x2 + -1y2)(x2 + 2y2) = 0

Factor a difference between two squares.
((x + y)(x + -1y))(x2 + 2y2) = 0


Subproblem 1
Set the factor '(x2 + 2y2)' equal to zero and attempt to solve:

Simplifying
x2 + 2y2 = 0

Solving
x2 + 2y2 = 0

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

Add '-2y2' to each side of the equation.
x2 + 2y2 + -2y2 = 0 + -2y2

Combine like terms: 2y2 + -2y2 = 0
x2 + 0 = 0 + -2y2
x2 = 0 + -2y2
Remove the zero:
x2 = -2y2

Simplifying
x2 = -2y2

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 '(x + y)' equal to zero and attempt to solve:

Simplifying
x + y = 0

Solving
x + y = 0

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

Add '-1y' to each side of the equation.
x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
x + 0 = 0 + -1y
x = 0 + -1y
Remove the zero:
x = -1y

Simplifying
x = -1y

Subproblem 3
Set the factor '(x + -1y)' equal to zero and attempt to solve:

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

Simplifying
x = y
Solution
x = {-1y, y}

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