a) (x-1)^5=(x-1)^3 b) (X^5)^2=X^13 trên x^4 (x khác 0) c) (x-2)^6 = (x-2)^4 CÁC BẠN HỘ MÌNH VỚI MÌNH ĐANG CẦN GẤP

0 bình luận về “a) (x-1)^5=(x-1)^3 b) (X^5)^2=X^13 trên x^4 (x khác 0) c) (x-2)^6 = (x-2)^4 CÁC BẠN HỘ MÌNH VỚI MÌNH ĐANG CẦN GẤP”

1. Giải thích các bước giải:

    a) `(x-1)^5=(x-1)^3`

   `=>(x-1)^5-(x-1)^3=0`

   `=>(x-1)^3[(x-1)^2-1]=0`

   `=>`\(\left[ \begin{array}{l}(x-1)^3=0\\(x-1)^2-1=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x-1=0\\(x-1)^2=1\end{array} \right.\)

   `=>`\(\left[ \begin{array}{l}x=0\\\left[ \begin{array}{l}x-1=1\\x-1=-1\end{array} \right.\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=0\\x=1\end{array} \right.\)

    b) `(x^5)^2=x^13/x^4`

   `=>x^10=x^9`

   `=>x^10-x^9=0`

   `=>x^9(x-1)=0`

   `=>`\(\left[ \begin{array}{l}x^9=0\\x-1=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=0\text{ (loại vì }x\ne0)\\x=1\end{array} \right.\)

    c) `(x-2)^6=(x-2)^4`

   `=>(x-2)^6-(x-2)^4=0`

   `=>(x-2)^4[(x-2)^2-1]=0`

   `=>`\(\left[ \begin{array}{l}(x-2)^4=0\\(x-2)^2-1=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x-2=0\\(x-2)^2=1\end{array} \right.\)

   `=>`\(\left[ \begin{array}{l}x=0\\\left[ \begin{array}{l}x-2=1\\x-2=-1\end{array} \right.\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=0\\x=3\\x=1\end{array} \right.\)

   Bình luận

2. $\begin{array}{l} a) \,(x-1)^5 = (x-1)^3\\ \Leftrightarrow (x-1)^5 – (x-1)^3 = 0\\ \Leftrightarrow (x-1)^3[(x-1)^2 – 1] = 0\\ \Leftrightarrow \left[\begin{array}{l}(x-1)^3 = 0\\(x-1)^2 – 1 =0\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x – 1 = 0\\(x-1)^2=1\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x =1\\x – 1 = 1\\x – 1 = -1\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x =1\\x =2\\x =0\end{array}\right.\\ b)\,(x^5)^2 = \dfrac{x^{13}}{x^4}\qquad (x \ne 0)\\ \Leftrightarrow x^{10} = x^9\\ \Leftrightarrow x^{10} – x^9 = 0\\ \Leftrightarrow x^9(x – 1) = 0\\ \Leftrightarrow \left[\begin{array}{l}x^9 = 0\\x – 1 = 0\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x=0 \quad (loại)\\x =1 \quad (nhận)\end{array}\right.\\ c)\,(x-2)^6 = (x-2)^4\\ \Leftrightarrow (x-2)^6 – (x-2)^4 = 0\\ \Leftrightarrow (x-2)^4[(x-2)^2 – 1] = 0\\ \Leftrightarrow \left[\begin{array}{l}(x-2)^4 = 0\\(x-2)^2 – 1=0\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x-2 = 0\\(x-2)^2 =1\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x=2\\x – 2 = 1\\x – 2 = -1\end{array}\right.\\ \Leftrightarrow \left[\begin{array}{l}x=2\\x =3\\x =1\end{array}\right.\\ \end{array}$

    

   Bình luận