Question

Rozwiąż równania:

1. 5x^3-x^2-20x+4=0

2. x^3+7x^2-21x-27=0

Answer 1

1.

5x^3-x^2-20x+4=0

x^2(5x - 1) - 4(5x - 1) = 0

(5x - 1)(x^2 - 4) = 0

(5x - 1)(x - 2)(x + 2) = 0

5x - 1 = 0   lub   x - 2 = 0   lub   x + 2 = 0

x = 1/5                 x = 2                x = -2

 

2.

x^3+7x^2-21x-27=0

x^3 - 27 + 7x^2 - 21x = 0

(x - 3)(x^2 + 3x + 9) + 7x(x - 3) = 0

(x - 3(x^2 + 3x + 9  + 7x) = 0

(x - 3)(x^2 + 10x + 9) =0

x - 3 = 0   lub  x^2 + 10x + 9 = 0

x = 3      lub     Δ = 100 - 36 = 64

                       √Δ = 8

                       x1 = (-10 - 8)/2 = -9

                       x2 = (-10 + 8)/2 = -1

odp. x = 3  lub x = -1  lub x = -9