Đáp án: $x^3+3x^2+3x=0$ $⇔x(x^2+3x+3)=0$ $⇔x^2+3x+3=0$ $⇔x^2 +2 .x \dfrac{3}{2} + \dfrac{9}{4} + \dfrac{3}{4}=0$ $⇔(x+\dfrac{3}{2})^2 +\dfrac{3}{4} > 0 ∀ x$ (loại) $⇔x=0$ Vậy $x=0$ ____________________ $x^3=4x$ $⇔x^3-4x=0$ $⇔x^3-2x^2+2x^2-4x=0$ $⇔x^2(x-2)+2x(x-2)=0$ $⇔(x-2)(x^2+2x)=0$ $⇔x(x+2)(x-2)=0$ ⇔\(\left[ \begin{array}{l}x=0\\x+2=0\\x-2=0\end{array} \right.\) ⇔\(\left[ \begin{array}{l}x=0\\x=-2\\x=2\end{array} \right.\) Vậy $\text{x ∈ {0 ; 2 ; -2} }$ ___________________________ $x^3-49x=0$ $⇔x^3-7x^2+7x^2-49x=0$ $⇔x^2(x-7)+7x(x-7)=0$ $⇔(x-7)(x^2+7x)=0$ $⇔x(x+7)(x-7)=0$ ⇔\(\left[ \begin{array}{l}x=0\\x+7=0\\x-7=0\end{array} \right.\) ⇔\(\left[ \begin{array}{l}x=0\\x=-7\\x=7\end{array} \right.\) Vậy $\text{ x ∈ {0 ; -7 ; 7 } }$ Reply
Giải thích các bước giải: `x^3+3x^2+3x=0` `=>(x^3+3x^2+3x+1)-1=0` `=>(x+1)^3=1` `=>x+1=1` `=>x=0` `x^3=4x` `=>x^3-4x=0` `=>x(x^2-4)=0` `=>x(x-2)(x+2)=0` `=>`\(\left[ \begin{array}{l}x=0\\x-2=0\\x+2=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=0\\x=2\\x=-2\end{array} \right.\) `x^3-49x=0` `=>x(x^2-49)=0` `=>x(x-7)(x+7)=0` `=>`\(\left[ \begin{array}{l}x=0\\x-7=0\\x+7=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=0\\x=7\\x=-7\end{array} \right.\) Reply
Đáp án:
$x^3+3x^2+3x=0$
$⇔x(x^2+3x+3)=0$
$⇔x^2+3x+3=0$
$⇔x^2 +2 .x \dfrac{3}{2} + \dfrac{9}{4} + \dfrac{3}{4}=0$
$⇔(x+\dfrac{3}{2})^2 +\dfrac{3}{4} > 0 ∀ x$ (loại)
$⇔x=0$
Vậy $x=0$
____________________
$x^3=4x$
$⇔x^3-4x=0$
$⇔x^3-2x^2+2x^2-4x=0$
$⇔x^2(x-2)+2x(x-2)=0$
$⇔(x-2)(x^2+2x)=0$
$⇔x(x+2)(x-2)=0$
⇔\(\left[ \begin{array}{l}x=0\\x+2=0\\x-2=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x=-2\\x=2\end{array} \right.\)
Vậy $\text{x ∈ {0 ; 2 ; -2} }$
___________________________
$x^3-49x=0$
$⇔x^3-7x^2+7x^2-49x=0$
$⇔x^2(x-7)+7x(x-7)=0$
$⇔(x-7)(x^2+7x)=0$
$⇔x(x+7)(x-7)=0$
⇔\(\left[ \begin{array}{l}x=0\\x+7=0\\x-7=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x=-7\\x=7\end{array} \right.\)
Vậy $\text{ x ∈ {0 ; -7 ; 7 } }$
Giải thích các bước giải:
`x^3+3x^2+3x=0`
`=>(x^3+3x^2+3x+1)-1=0`
`=>(x+1)^3=1`
`=>x+1=1`
`=>x=0`
`x^3=4x`
`=>x^3-4x=0`
`=>x(x^2-4)=0`
`=>x(x-2)(x+2)=0`
`=>`\(\left[ \begin{array}{l}x=0\\x-2=0\\x+2=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=0\\x=2\\x=-2\end{array} \right.\)
`x^3-49x=0`
`=>x(x^2-49)=0`
`=>x(x-7)(x+7)=0`
`=>`\(\left[ \begin{array}{l}x=0\\x-7=0\\x+7=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=0\\x=7\\x=-7\end{array} \right.\)