Zad. 4
a)
x(x² - 4x) = 0
x²(x - 4) = 0
x² = 0 lub x - 4 = 0
x = 0 lub x = 4
Odp. x = 0 lub x = 4
b)
x(4x²+ x) = 0
x²(4x + 1) = 0
x² = 0 lub 4x + 1 = 0
x = 0 lub 4x = - 1 |:4
x = 0 lub x = - ¹/₄
Odp. x = - ¹/₄ lub x = 0
c)
(x²- x)(x + 2) = 0
x(x - 1)(x + 2) = 0
x = 0 lub x - 1 = 0 lub x + 2 = 0
x = 0 lub x = 1 lub x = - 2
Odp. x = - 2 lub x = 0 lub x = 1
d)
(x² + x)(x - 6) = 0
x(x + 1)(x - 6) = 0
x = 0 lub x + 1 = 0 lub x - 6 = 0
x = 0 lub x = - 1 lub x = 6
Odp. x = - 1 lub x = 0 lub x = 6
e)
(2x² - x)(2x + 1) = 0
x(2x - 1)(2x + 1) = 0
x = 0 lub 2x - 1 = 0 lub 2x + 1 = 0
x = 0 lub 2x = 1 |:2 lub 2x = - 1 |:2
x = 0 lub x = ¹/₂ lub x = - ¹/₂
Odp. x = - ¹/₂ lub x = 0 lub x = ¹/₂
f)
(4x² - x)(6x - 2) = 0
2x(4x - 1)(3x - 1) = 0
2x = 0 |:2 lub 4x - 1 = 0 lub 3x - 1 = 0
x = 0 lub 4x = 1 |:4 lub 3x = 1 |:3
x = 0 lub x = ¹/₄ lub x = ¹/₃
Odp. x = 0 lub x = ¹/₄ lub x = ¹/₃
