a) $(x-1)^3$=343
$=>(x-1)^3=7^3$
$=>x-1=7$
$=>x=8$
b) (số sai rồi nha bạn, ra lẻ lắm)
c) $(x-4)^2=(x-4)^4$
$=>(x-4)^4-(x-4)^2=0$
$=>(x-4)^2[(x-4)^2-1]=0$
\(=>\left[{}\begin{matrix}\left(x-4\right)^2=0\\\left(x-4\right)^2-1=0\end{matrix}\right.\)
\(=>\left[{}\begin{matrix}\left(x-4\right)^2=0\\\left(x-4\right)^2=1\end{matrix}\right.\)
\(=>\left[{}\begin{matrix}x-4=0\\x-4=1\\x-4=-1\end{matrix}\right.\)
\(=>\left[{}\begin{matrix}x=4\\x=5\\x=3\end{matrix}\right.\)
a,\(\left(x-1\right)^3=343\)
\(\Rightarrow x-1=7\Rightarrow x=8\)
b, \(\left(x-2\right)^4=4096\)
\(\Rightarrow x-2=8\Rightarrow x=10\)
c, \(\left(x-4\right)^2=\left(x-4\right)^4\)
\(\Rightarrow\left(x-4\right)^2=\left[\left(x-4\right)^2\right]^2\)
\(\Rightarrow x-4=\left(x-4\right)^2\)
\(\Rightarrow\left(x-4\right)-\left(x-4\right)^2=0\)
\(\Rightarrow\left(x-4\right)\left(1-x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-4=0\\5-x=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=5\end{matrix}\right.\)
Chúc bạn học tốt!!!
\(\left(x-1\right)^3=343\)
\(\Rightarrow\left(x-1\right)^3=7^3\)
\(\Rightarrow x-1=7\Rightarrow x=8\)
\(\left(x-2\right)^4=4096\)
\(\Rightarrow\left(x-2\right)^4=\pm8^4\)
\(\Rightarrow\left[{}\begin{matrix}x-2=8\Rightarrow x=10\\x-2=-8\Rightarrow x=-6\end{matrix}\right.\)
\(\left(x-4\right)^2=\left(x-4\right)^4\)
\(\Rightarrow\left(x-4\right)^4-\left(x-4\right)^2=0\)
\(\Rightarrow\left(x-4\right)^2\left[\left(x-4\right)^2-1\right]=0\)
\(\Rightarrow\left\{{}\begin{matrix}\left(x-4\right)^2=0\\\left(x-4\right)^2=1\end{matrix}\right.\)
\(\Rightarrow x=4\)
\(\Rightarrow\left\{{}\begin{matrix}x-4=1\Rightarrow x=5\\x-4=-1\Rightarrow x=3\end{matrix}\right.\)
\(a,\left(x-1\right)^3=343\)
\(\Leftrightarrow\left(x-1\right)^3=7^3\)
\(\Leftrightarrow x-1=7\)
\(\Leftrightarrow x=8\)
Vậy ........
b) \(\left(x-2\right)^4=4069\)
\(\Leftrightarrow\left(x-2\right)^4=8^4\)
\(\Leftrightarrow x-2=8\)
\(\Leftrightarrow x=10\)
Vậy ..............
c) \(\left(x-4\right)^2=\left(x-4\right)^4\)
\(\Leftrightarrow\left(x-4\right)^2=\left[\left(x-4\right)^2\right]^2\)
\(\Leftrightarrow x-4=\left(x-4\right)^2\)
\(\Leftrightarrow\left(x-4\right)-\left(x-4\right)^2=0\)
\(\Leftrightarrow x-4-\left(1-x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\5-x=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=5\end{matrix}\right.\)
Vậy ...
a) \(\left(x-1\right)^3=343\)
\(\Leftrightarrow\left(x-1\right)^3=7^3\)
\(\Leftrightarrow x-1=7\Leftrightarrow x=8\)
Vậy x = 8.
b) \(\left(x-2\right)^4=4096\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=8\\x-2=-8\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-6\end{matrix}\right.\)
Vậy x1 = 10; x2 = -6.
c) \(\left(x-4\right)^2=\left(x-4\right)^4\)
\(\Leftrightarrow\left(x-4\right)^2-\left(x-4\right)^4=0\)
\(\Leftrightarrow\left(x-4\right)^2\left[1-\left(x-2\right)^2\right]=0\)
\(\Leftrightarrow\left(x-4\right)^2\left(1-x+2\right)\left(1+x-2\right)=0\)
\(\Leftrightarrow\left(x-4\right)^2\left(3-x\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-4\right)^2=0\\3-x=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=3\\x=1\end{matrix}\right.\)
Vậy x1 = 4; x2 = 3; x3 = 1.
