x^3+3x^2+3x=0 x^3=4x x^3-49x=0

x^3+3x^2+3x=0
x^3=4x
x^3-49x=0

0 thoughts on “x^3+3x^2+3x=0 x^3=4x x^3-49x=0”

  1. 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
  2. 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

Leave a Comment