Question

Rozwiąż równanie: 4x^3 - 6x^2 + 2 = 0

Answer 1

(4x)³ - (6x)² + 2 = 0
(4x x 4x x 4x) - (6x x 6x) + 2 = 0
64 x - 36 x + 2 = 0
28 x + 2 = 0
x = - 1/14

Answer 2

4x^3 - 6x^2 + 2 = 0

4x³ - 4x² - 2x² + 2 = 0

4x²(x - 1) - 2(x² - 1) = 0

4x²(x - 1) - 2(x - 1)(x + 1) = 0

(x - 1) [ (4x² - 2(x + 1)] = 0

(x - 1)(4x² - 2x - 2) = 0

x - 1 = 0   lub   4x² - 2x - 2 = 0

x = 1                   Δ = 4 - 4 * 4 * (-2) = 4 + 32 = 36

                            √Δ = 6

                            x1 = (2 - 6)/8 = -4/8 = -1/2

                            x2 = (2 + 6)/8 = 8/8 = 1

odp.  x = 1  lub  x = -1/2    lub    x = 1