4x⁴ = 1 - 3x²
4x⁴ + 3x² - 1 = 0
Factor the left side:
(4x² - 1) (x² + 1) = 0
((2x)² - 1²) (x² - i ²) = 0
(2x + 1) (2x - 1) (x - i ) (x + i ) = 0
Then
2x + 1 = 0 or 2x - 1 = 0 or x - i = 0 or x + i = 0
Solve for x :
x = -1/2 or x = 1/2 or x = i or x = -i
