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Simplifying y8 + -8y4 + 16 = 0 Reorder the terms: 16 + -8y4 + y8 = 0 Solving 16 + -8y4 + y8 = 0 Solving for variable 'y'. Factor a trinomial. (4 + -1y4)(4 + -1y4) = 0 Factor a difference between two squares. ((2 + y2)(2 + -1y2))(4 + -1y4) = 0 Factor a difference between two squares. ((2 + y2)(2 + -1y2))(2 + y2)(2 + -1y2) = 0Subproblem 1
Set the factor '(2 + y2)' equal to zero and attempt to solve: Simplifying 2 + y2 = 0 Solving 2 + y2 = 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 + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y2 = 0 + -2 y2 = 0 + -2 Combine like terms: 0 + -2 = -2 y2 = -2 Simplifying y2 = -2 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 '(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 3
Set the factor '(2 + y2)' equal to zero and attempt to solve: Simplifying 2 + y2 = 0 Solving 2 + y2 = 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 + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y2 = 0 + -2 y2 = 0 + -2 Combine like terms: 0 + -2 = -2 y2 = -2 Simplifying y2 = -2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
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}Solution
y = {-1.414213562, 1.414213562, -1.414213562, 1.414213562}
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