solve for x : 16x2 - 8a2x + (a4-b4) = 0

Given : 16x2 - 8a2x + (a4 - b4) = 0

⇒ 16x2 - 4(a2 + b2) x - 4(a2 - b2) x + (a4 - b4) = 0

⇒ 4x(4x - (a2 + b2)) - (a2 - b2)(4x - (a2 + b2)) = 0

⇒ (4x - (a2 + b2))(4x - (a2 - b2)) = 0

⇒ 4x = a2 + b2 or a2 - b2

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