x^4-17x^2y^2+72y^4=0

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Solution for x^4-17x^2y^2+72y^4=0 equation: 


Simplifying
x4 + -17x2y2 + 72y4 = 0

Reorder the terms:
-17x2y2 + x4 + 72y4 = 0

Solving
-17x2y2 + x4 + 72y4 = 0

Solving for variable 'x'.

Factor a trinomial.
(x2 + -9y2)(x2 + -8y2) = 0

Factor a difference between two squares.
((x + 3y)(x + -3y))(x2 + -8y2) = 0


Subproblem 1
Set the factor '(x2 + -8y2)' equal to zero and attempt to solve:

Simplifying
x2 + -8y2 = 0

Solving
x2 + -8y2 = 0

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

Add '8y2' to each side of the equation.
x2 + -8y2 + 8y2 = 0 + 8y2

Combine like terms: -8y2 + 8y2 = 0
x2 + 0 = 0 + 8y2
x2 = 0 + 8y2
Remove the zero:
x2 = 8y2

Simplifying
x2 = 8y2

Take the square root of each side:
x = {-2.828427125y, 2.828427125y}

Subproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve:

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

Add '-3y' to each side of the equation.
x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
x + 0 = 0 + -3y
x = 0 + -3y
Remove the zero:
x = -3y

Simplifying
x = -3y

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

Simplifying
x + -3y = 0

Solving
x + -3y = 0

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

Add '3y' to each side of the equation.
x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
x + 0 = 0 + 3y
x = 0 + 3y
Remove the zero:
x = 3y

Simplifying
x = 3y
Solution
x = {-2.828427125y, 2.828427125y, -3y, 3y}

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