Y^4+X^4-2X^2=0

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Solution for Y^4+X^4-2X^2=0 equation: 


Simplifying
Y4 + X4 + -2X2 = 0

Reorder the terms:
-2X2 + X4 + Y4 = 0

Solving
-2X2 + X4 + Y4 = 0

Solving for variable 'X'.

Factor a trinomial.
(X2 + -1Y2)(X2 + -1Y2) = 0

Factor a difference between two squares.
((X + Y)(X + -1Y))(X2 + -1Y2) = 0

Factor a difference between two squares.
((X + Y)(X + -1Y))(X + Y)(X + -1Y) = 0


Subproblem 1
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 2
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

Subproblem 3
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 4
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, -1Y, Y}

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