x^4-2y^4=1

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Solution for x^4-2y^4=1 equation: 


Simplifying
x4 + -2y4 = 1

Solving
x4 + -2y4 = 1

Solving for variable 'x'.

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

Add '2y4' to each side of the equation.
x4 + -2y4 + 2y4 = 1 + 2y4

Combine like terms: -2y4 + 2y4 = 0
x4 + 0 = 1 + 2y4
x4 = 1 + 2y4

Simplifying
x4 = 1 + 2y4

Reorder the terms:
-1 + x4 + -2y4 = 1 + 2y4 + -1 + -2y4

Reorder the terms:
-1 + x4 + -2y4 = 1 + -1 + 2y4 + -2y4

Combine like terms: 1 + -1 = 0
-1 + x4 + -2y4 = 0 + 2y4 + -2y4
-1 + x4 + -2y4 = 2y4 + -2y4

Combine like terms: 2y4 + -2y4 = 0
-1 + x4 + -2y4 = 0

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

Take the square root of each side:
x = {-1.414213562y, 1.414213562y}

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

Simplifying
x2 + y2 = 0

Solving
x2 + y2 = 0

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

Add '-1y2' to each side of the equation.
x2 + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
x2 + 0 = 0 + -1y2
x2 = 0 + -1y2
Remove the zero:
x2 = -1y2

Simplifying
x2 = -1y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-1.414213562y, 1.414213562y}

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