`1` Tìm `x` `a). (x-1).(x+2)-2x(x-1)=0` `b).(x-4).(2x+1)-x^2+16=0` `c). x^3-16x=0`

Đáp án`+`Giải thích các bước giải:

 ` a) (x-1)(x+2)-2x(x-1)=0 `

` ⇔ (x-1)(x+2-2x)=0 `

` ⇔ (x-1)(2-x)=0 `

`⇔` $\left[\begin{matrix} x-1=0\\2-x=0\end{matrix}\right.$

`⇔` $\left[\begin{matrix} x=1\\x=2\end{matrix}\right.$

Vậy `x ∈ {1;2}`

 ` b) (x-4)(2x+1)-x^2+16=0 `

` ⇔ (x-4)(2x+1)-(x^2-4^2)=0 `

` ⇔ (x-4)(2x+1)-(x-4)(x+4)=0 `

` ⇔ (x-4)[2x+1-(x+4)]=0 `

` ⇔ (x-4)(2x+1-x-4)=0 `

` ⇔ (x-4)(x-3)=0 `

`⇔` $\left[\begin{matrix} x-4=0\\x-3=0\end{matrix}\right.$

`⇔` $\left[\begin{matrix} x=4\\x=3\end{matrix}\right.$

Vậy `x∈ {4;3}`

 `c) x^3-16x=0 `

` ⇔ x(x^2-16)=0 `

` ⇔ x(x^2-4^2)=0 `

` ⇔ x(x-4)(x+4)=0`

`⇔` $\left[\begin{matrix} x=0\\x-4=0\\x+4=0\end{matrix}\right.$

`⇔` $\left[\begin{matrix} x=0\\x=4\\x=-4\end{matrix}\right.$

Vậy `x ∈ {0;±4}`