Question

Tìm x, biết

\(\left(x-1\right)^3-x\left(x-2\right)^2=-1\)

Answer 1

`(x-1)^3 - x(x-2)^2 = -1`

`=> (x^3 - 3x^2 + 3x - 1) - x(x^2 - 4x + 4) +1 = 0`

`=> (x^3 - 3x^2 + 3x - 1) - (x^3 - 4x^2 + 4x) +1 = 0`

`=> x^3 - 3x^2 + 3x - 1 -x^3 +4x^2 - 4x +1 = 0`

`=> x^2 - x = 0`

`=> x(x-1) = 0`

`=> x = 0` hoặc `x = 1`

Vậy ...

Answer 2

\(\left(x-1\right)^3-x\left(x-2\right)^2=-1\)

\(\Leftrightarrow x^3-3x^2+3x-1-x^3+4x^2-4x+1=0\)

\(\Leftrightarrow x^2-x=0\)

\(\Leftrightarrow x\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)