Question

4x3 - 13x2-13x+4=0 rozwiąż równanie

Answer 1

4x³+4 -13x²-13x=0

4(x³+1)-13x(x+1)=0

4(x+1)(x²-x+1)-13x(x+1)=0

(x+1)(4x²-4x+4 -13x)=0

x+1=0  ∨ 4x²-17x+4=0

x= -1     ∨  Δ=289-64=225

                    √Δ=15

                  x₁=¼

                  x₂=4

 

Answer 2

4x^3 - 13x^2 - 13x + 4 = 0

4(x^3 + 1) - 13x(x + 1) = 0

4(x + 1)(x^2 -x + 1) - 13x(x + 1) = 0

(x  +1) [ 4(x^2 - x + 1) - 13x ] = 0

x + 1 = 0    lub  4x^2 - 4x + 4 - 13x = 0

x = -1                  4x^2 - 17x + 4 = 0

                            Δ = 289 - 64 = 225

                            √Δ = 15

                             x1 = (17 - 15)/8 = 2/8 = 1/4

                              x2 = (17 + 15)/8 = 32/8 = 4

 

odp. x = -1  lub  x = 1/4   lub  x =  4