Tìm số hữu tỉ x, biết rằng : (2x – 1)^6 = (2x – 1)^8 01/09/2021 Bởi Parker Tìm số hữu tỉ x, biết rằng : (2x – 1)^6 = (2x – 1)^8
$(2x-1)^6 = (2x – 1)^8$ $⇔(2x-1)^8 – (2x – 1)^6 = 0$ $⇔(2x-1)^6[(2x-1)^2 – 1] = 0$ ⇔\(\left[ \begin{array}{l}(2x-1)^6=0\\(2x-1)^2 -1=0\end{array} \right.\) ⇔\(\left[ \begin{array}{l}2x-1=0\\(2x-1)^2 = 1\end{array} \right.\) ⇔ \(\left[ \begin{array}{l}2x-1=0\\2x-1 = 1\\2x-1=-1\end{array} \right.\) ⇔ \(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=1\\x=0\end{array} \right.\) Bình luận
Đáp án: `(2x-1)^6=(2x-1)^8` `<=>(2x-1)^8-(2x-1)^6=0` `<=>(2x-1)^6[(2x-1)^2-1]=0` `<=>` \(\left[ \begin{array}{l}(2x-1)^6=0\\(2x-1)^2=1\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}2x-1=0\\2x-1=1\\2x-1=-1\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}2x=1\\2x=2\\2x=0\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=\dfrac12\\x=1\\x=0\end{array} \right.\) Vậy `x=0,x=1` hoặc `x=1/2.` Bình luận
$(2x-1)^6 = (2x – 1)^8$
$⇔(2x-1)^8 – (2x – 1)^6 = 0$
$⇔(2x-1)^6[(2x-1)^2 – 1] = 0$
⇔\(\left[ \begin{array}{l}(2x-1)^6=0\\(2x-1)^2 -1=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}2x-1=0\\(2x-1)^2 = 1\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}2x-1=0\\2x-1 = 1\\2x-1=-1\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=1\\x=0\end{array} \right.\)
Đáp án:
`(2x-1)^6=(2x-1)^8`
`<=>(2x-1)^8-(2x-1)^6=0`
`<=>(2x-1)^6[(2x-1)^2-1]=0`
`<=>` \(\left[ \begin{array}{l}(2x-1)^6=0\\(2x-1)^2=1\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}2x-1=0\\2x-1=1\\2x-1=-1\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}2x=1\\2x=2\\2x=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\dfrac12\\x=1\\x=0\end{array} \right.\)
Vậy `x=0,x=1` hoặc `x=1/2.`