a)
x³ - 4x² + 3x = 0
x³ - x² - 3x² + 3x = 0
x²(x-1) - 3x(x-1) = 0
(x² - 3x)(x-1) = 0
x(x-3)(x-1) = 0
x = 0 ∨ x-3 = 0 ∨ x-1 = 0
x = 0 ∨ x = 3 ∨ x = 1
Odp. x∈{0, 1, 3}
b)
2x⁴- 5x³ - 2x² + 10x - 4 = 0
2x₄- 4x² - x³ + 2x - 4x³ + 8x + 2x² - 4 = 0
2x²(x²-2) - x(x²-2) - 4x(x²-2) + 2(x²-2) = 0
(x²-2)(2x² - x - 4x + 2) = 0
(x²-2)(2x² - 4x - x + 2) = 0
(x²-2)(2x(x-2) - 1(x-2)) = 0
(x²-2)(2x-1)(x-2) = 0
(x+√2)(x-√2)(x-½)(x-2) = 0
x = -√2 ∨ x = √2 ∨ x = ½ ∨ x = 2
Odp. x∈{-√2, ½, √2, 2}
