Toán Tìm x biết: (x- 2)( x^2+ 2x+ 5)+ 2(x- 2)( x+ 2)- 5(x- 2)= 0 01/07/2021 By Ximena Tìm x biết: (x- 2)( x^2+ 2x+ 5)+ 2(x- 2)( x+ 2)- 5(x- 2)= 0
`(x – 2)(x^2 + 2x + 5) + 2(x – 2)(x + 2) – 5(x – 2) = 0` `<=> (x – 2)(x^2 + 2x + 5 + 2x + 4 – 5) = 0` `<=> (x – 2)(x^2 + 4x + 4) = 0` `<=> (x – 2)(x + 2)^2 = 0` `<=>` \(\left[ \begin{array}{l}x – 2 = 0\\x + 2 = 0\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x = 2\\x = -2\end{array} \right.\) `=> x = +-2` Trả lời
Đáp án: $x∈\{2;-2\}$ Giải thích các bước giải: $(x-2)(x^2+2x+5)+2(x-2)(x+2)-5(x-2)=0$ $⇔(x-2)(x^2+2x+5)+(x-2)(2x+4)-5(x-2)=0$ $⇔(x-2)(x^2+2x+5+2x+4-5)=0$ $⇔(x-2)(x^2+4x+4)=0$ $⇔(x-2)(x+2)^2=0$ $⇔\left[ \begin{array}{l}x-2=0\\(x+2)^2=0\end{array} \right.$ $⇔\left[ \begin{array}{l}x-2=0\\x+2=0\end{array} \right.$ $⇔\left[ \begin{array}{l}x=2\\x=-2\end{array} \right.$ Vậy $x∈\{2;-2\}$ Trả lời
`(x – 2)(x^2 + 2x + 5) + 2(x – 2)(x + 2) – 5(x – 2) = 0`
`<=> (x – 2)(x^2 + 2x + 5 + 2x + 4 – 5) = 0`
`<=> (x – 2)(x^2 + 4x + 4) = 0`
`<=> (x – 2)(x + 2)^2 = 0`
`<=>` \(\left[ \begin{array}{l}x – 2 = 0\\x + 2 = 0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x = 2\\x = -2\end{array} \right.\)
`=> x = +-2`
Đáp án: $x∈\{2;-2\}$
Giải thích các bước giải:
$(x-2)(x^2+2x+5)+2(x-2)(x+2)-5(x-2)=0$
$⇔(x-2)(x^2+2x+5)+(x-2)(2x+4)-5(x-2)=0$
$⇔(x-2)(x^2+2x+5+2x+4-5)=0$
$⇔(x-2)(x^2+4x+4)=0$
$⇔(x-2)(x+2)^2=0$
$⇔\left[ \begin{array}{l}x-2=0\\(x+2)^2=0\end{array} \right.$
$⇔\left[ \begin{array}{l}x-2=0\\x+2=0\end{array} \right.$
$⇔\left[ \begin{array}{l}x=2\\x=-2\end{array} \right.$
Vậy $x∈\{2;-2\}$