Question

Tìm x, biết:
6) x^3 - 2x^2 + 2x = 0
7) 2x^3 - 5x^2 + 8x - 5 = 0

Answer 1

\(x^3-2x^2+2x=0\)

\(\Rightarrow x\left(x^2-2x+2\right)=0\)

\(\Rightarrow x\left(x^2-2.x.1+1^2+1\right)=0\)

\(\Rightarrow x\left[\left(x-1\right)^2+1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\\left(x-1\right)^2+1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\\left(x-1\right)^2=-1\end{matrix}\right.\Rightarrow x=0\)

Answer 2

\(2x^3-5x^2+8x-5=0\)

\(\Rightarrow2x^3-3x^2-2x^2+5x+3x-5=0\)

\(\Rightarrow\left(2x^3-2x^2\right)-\left(3x^2-3x\right)+\left(5x-5\right)=0\)

\(\Rightarrow2x^2\left(x-1\right)-3x\left(x-1\right)+5\left(x-1\right)=0\)

\(\Rightarrow\left(x-1\right)\left(2x^2-3x+5\right)\)