y^4-3y^2+2=0

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Solution for y^4-3y^2+2=0 equation: 


Simplifying
y4 + -3y2 + 2 = 0

Reorder the terms:
2 + -3y2 + y4 = 0

Solving
2 + -3y2 + y4 = 0

Solving for variable 'y'.

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

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


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

Simplifying
2 + -1y2 = 0

Solving
2 + -1y2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y2 = 0 + -2
-1y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1y2 = -2

Divide each side by '-1'.
y2 = 2

Simplifying
y2 = 2

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

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

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

Combine like terms: 1 + -1 = 0
0 + y = 0 + -1
y = 0 + -1

Combine like terms: 0 + -1 = -1
y = -1

Simplifying
y = -1

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1y = 0 + -1
-1y = 0 + -1

Combine like terms: 0 + -1 = -1
-1y = -1

Divide each side by '-1'.
y = 1

Simplifying
y = 1
Solution
y = {-1.414213562, 1.414213562, -1, 1}

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