Cubic Equation

[MathWarrior]

Equation 1:
Find all real $x$ that are solutions of the equation
[tex]x^{3} - 5x^{2}+10x-12 = 0[/tex]

Equation 2:
To prove that:
[tex]a, b, c \in R[/tex], [tex]a + b + c = 0[/tex] [tex]\Rightarrow[/tex]
[tex]a^{3}+b^{3}+c^{3}=3abc[/tex]

[Guest]

[tex]x^3−5x^2+10x−12=(x-3)(x^2-2x+4)[/tex]

[red12dog34]

[tex]a^3+b^3+c^3=\dfrac{1}{2}(a+b+c)\left[(a-b)^2+(b-c)^2+(c-a)^2\right]+3abc[/tex]