a, \(\left|2x-1\right|=x+4\)
\(\orbr{\begin{cases}2x-1=x+4\\-2x+1=x+4\end{cases}\Rightarrow\orbr{\begin{cases}x-5=0\\-3x-3=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=5\\x=-1\end{cases}}}\)
b, \(\left(3x-1\right)^4=81\)
\(\left(3x-1\right)^4=3^4\Leftrightarrow\orbr{\begin{cases}3x-1=3\\3x-1=-3\end{cases}\Leftrightarrow\orbr{\begin{cases}3x-4=0\\3x+2=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=\frac{4}{3}\\x=-\frac{2}{3}\end{cases}}}\)
c, \(\left(x-2\right)^3=-64\)
\(\left(x-2\right)^3=\left(-4\right)^3\Leftrightarrow x-2=-4\Leftrightarrow x=-2\)
d, chia 2 TH làm như phần a đó, chắc vậy :v
Bài làm
a) \(\left|2x-1\right|=x+4\)
\(\Rightarrow\orbr{\begin{cases}2x-1=x+4\\2x-1=-x-4\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=-1\end{cases}}}\)
Vậy x = { 5; -1 }
b) \(\left(3x-1\right)^4=81\)
\(\Rightarrow\left(3x-1\right)^4=\left(\pm3\right)^8\)
\(\Rightarrow\orbr{\begin{cases}3x-1=3\\3x-1=-3\end{cases}\Rightarrow\orbr{\begin{cases}3x=4\\3x=-2\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{4}{3}\\x=-\frac{2}{3}\end{cases}}}\)
Vậy x = { -4/2; -2/3 }
c) \(\left(x-2\right)^3=-64\)
\(\Rightarrow\left(x-2\right)^3=-4^3\)
\(\Rightarrow x-2=-4\)
\(\Rightarrow x=-2\)
d) \(\left|x-3\right|-\left|2x-1\right|=0\)
\(\Rightarrow\left|x-3\right|=\left|2x-1\right|\)
\(\Rightarrow\orbr{\begin{cases}x-3=2x-1\\x-3=-2x+1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}-x=2\\3x=4\end{cases}\Rightarrow\orbr{\begin{cases}x=-2\\x=\frac{4}{3}\end{cases}}}\)
Vậy x = { -2; 4/3 }
