Tìm x biết: ($x^{3}$ -1):(x-1)-( $9x^{2}$ -1):(3x-1)=0 21/08/2021 Bởi Natalia Tìm x biết: ($x^{3}$ -1):(x-1)-( $9x^{2}$ -1):(3x-1)=0
(x³ -1):(x-1)-(9x²-1):(3x-1)=0 (=)(x -1)(x²+x+1):(x-1)-(3x-1)(3x+1):(3x-1)=0 (=)x²+x+1-3x-1=0 (=)x²-2x=0 (=)x(x-2)=0 (=)\(\left[ \begin{array}{l}x=0\\x-2=0\end{array} \right.\) (=)\(\left[ \begin{array}{l}x=0\\x=2\end{array} \right.\) S={2;0} Bình luận
Đáp án:Tham khảo Giải thích các bước giải: $\text{ĐK}$:\(\left[ \begin{array}{l}:x-1\neq 0\\3x-1\neq 0\end{array} \right.\) ⇔\(\left[ \begin{array}{l}x\neq 1\\x\neq \dfrac{1}{3}\end{array} \right.\) $\text{Ta có:}$ $(x³-1):(x-1)-(9x²-1):(3x-1)=0$ $⇔(x-1)(x²+x+1):(x-1)-[(3x)²-1²]:(3x-1)=0$ $⇔(x-1)(x²+x+1):(x-1)-(3x-1)(3x+1):(3x-1)=0$ $⇔(x²+x+1)-(3x+1)=0$ $⇔x²+x+1-3x-1=0$ $⇔x²-2x=0$ $⇔x(x-2)=0$ ⇔\(\left[ \begin{array}{l}x=0\\x-2=0\end{array} \right.\) ⇔\(\left[ \begin{array}{l}x=0\\x=2\end{array} \right.\) $\text{Vậy x∈(0;2)}$ Bình luận
(x³ -1):(x-1)-(9x²-1):(3x-1)=0
(=)(x -1)(x²+x+1):(x-1)-(3x-1)(3x+1):(3x-1)=0
(=)x²+x+1-3x-1=0
(=)x²-2x=0
(=)x(x-2)=0
(=)\(\left[ \begin{array}{l}x=0\\x-2=0\end{array} \right.\) (=)\(\left[ \begin{array}{l}x=0\\x=2\end{array} \right.\)
S={2;0}
Đáp án:Tham khảo
Giải thích các bước giải:
$\text{ĐK}$:\(\left[ \begin{array}{l}:x-1\neq 0\\3x-1\neq 0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x\neq 1\\x\neq \dfrac{1}{3}\end{array} \right.\)
$\text{Ta có:}$
$(x³-1):(x-1)-(9x²-1):(3x-1)=0$
$⇔(x-1)(x²+x+1):(x-1)-[(3x)²-1²]:(3x-1)=0$
$⇔(x-1)(x²+x+1):(x-1)-(3x-1)(3x+1):(3x-1)=0$
$⇔(x²+x+1)-(3x+1)=0$
$⇔x²+x+1-3x-1=0$
$⇔x²-2x=0$
$⇔x(x-2)=0$
⇔\(\left[ \begin{array}{l}x=0\\x-2=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x=2\end{array} \right.\)
$\text{Vậy x∈(0;2)}$