Question

3x3 - 7x2 - 7x +3 = 0 rozwiąż równanie

Answer 1

3x³+3 -7x²-7x=0

3(x³+1) - 7x(x+1)=0

3(x+1)(x²-x+1)- 7x(x+1)=0

(x+1)[3(x²-x+1)- 7x]=0

 

(x+1)(3x² - 3x+3 - 7x)=0

(x+1)(3x²-10x+3)=0

x+1=0    ∨   3x²-10x+3=0

x= -1      ∨   Δ=100-4·3·3=100-36=64

              √Δ=8

            x₁=⅓

            x₂=3

Answer 2

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

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

3(x^3 + 1) - 7x(x + 1)=0

3(x+1)(x^2-x+1) - 7x(x + 1)=0

(x+1)(3(x^2-x+1) - 7x)=0

(x+1)(3x^2-10x+3)=0

x=-1   lub   3x^2-10x+3=0

                  delta= 100-36=64 => pierwiastek z delty = 8

                  x=(10-8)/6 =1/3 lub x=(10+8)/6 =3

 

Odp. x={-1,1/3,3}