a^4-10a^2b^2+16b^4=0

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Solution for a^4-10a^2b^2+16b^4=0 equation:


Simplifying
a4 + -10a2b2 + 16b4 = 0

Reorder the terms:
-10a2b2 + a4 + 16b4 = 0

Solving
-10a2b2 + a4 + 16b4 = 0

Solving for variable 'a'.

Factor a trinomial.
(a2 + -8b2)(a2 + -2b2) = 0

Subproblem 1

Set the factor '(a2 + -8b2)' equal to zero and attempt to solve: Simplifying a2 + -8b2 = 0 Solving a2 + -8b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '8b2' to each side of the equation. a2 + -8b2 + 8b2 = 0 + 8b2 Combine like terms: -8b2 + 8b2 = 0 a2 + 0 = 0 + 8b2 a2 = 0 + 8b2 Remove the zero: a2 = 8b2 Simplifying a2 = 8b2 Take the square root of each side: a = {-2.828427125b, 2.828427125b}

Subproblem 2

Set the factor '(a2 + -2b2)' equal to zero and attempt to solve: Simplifying a2 + -2b2 = 0 Solving a2 + -2b2 = 0 Move all terms containing a to the left, all other terms to the right. Add '2b2' to each side of the equation. a2 + -2b2 + 2b2 = 0 + 2b2 Combine like terms: -2b2 + 2b2 = 0 a2 + 0 = 0 + 2b2 a2 = 0 + 2b2 Remove the zero: a2 = 2b2 Simplifying a2 = 2b2 Take the square root of each side: a = {-1.414213562b, 1.414213562b}

Solution

a = {-2.828427125b, 2.828427125b, -1.414213562b, 1.414213562b}

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