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\((3x-1)+3^2=5^2\)
\(\Rightarrow(3x-1)^4+9=25\)
\(\Rightarrow(3x-1)^4=25-9\)
\(\Rightarrow(3x-1)^4=16\)
\(\Rightarrow(3x-1)=(-2)^4=2^4\)
\(\Rightarrow\hept{\begin{cases}3x-1=2\\3x-1=-2\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}3x=2+1\\3x=-2+1\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}3x=3\\3x=-1\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=3\div3\\x=-1\div3\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}x=1\\x=-\frac{1}{3}\end{cases}}\)
\(\left(x-1\right)^2=\left(x-1\right)^4\)
\(\left(x-1\right)^2-\left(x-1\right)^4=0\)
\(\left(x-1\right)^2-\left(x-1\right)^2\left(x-1\right)^2=0\)
\(\left(x-1\right)^2\left[1-\left(x-1\right)^2\right]=0\)
\(\left(x-1\right)^2\left(1-x+1\right)\left(1+x-1\right)=0\)
\(\left(x-1\right)^2\left(2-x\right)x=0\)
\(\Rightarrow\left(x-1\right)^2=0\)hoac \(\Rightarrow\orbr{\begin{cases}x=0\\2-x=0\end{cases}}\)
\(\Rightarrow x-1=0\) hoac \(\Rightarrow\orbr{\begin{cases}x=0\\x=2\end{cases}}\)
\(\Rightarrow x=1\)hoac \(\orbr{\begin{cases}x=0\\x=2\end{cases}}\)
\(\left(x-5\right)^3=\left(x-5\right)^{15}\)
\(\left(x-5\right)^3-\left(x-5\right)^{15}=0\)
\(\left(x-5\right)^3-\left(x-5\right)^3\left(x-5\right)^{12}=0\)
\(\left(x-5\right)^3\left[1-\left(x-5\right)^{12}\right]=0\)
Ta có : 2x + 2x + 1 = 24
=> 2x(1 + 2) = 24
=> 2x.3 = 24
=> 2x = 8
=> 2x = 23
=> x = 3
Ta có : (x + 2)4 = (x + 2)6
=> (x + 2)4 - (x + 2)6 = 0
<=> (x + 2)4 (1 - (x + 2)2) = 0
<=> \(\orbr{\begin{cases}\left(x+2\right)^4=0\\\left(1-\left(x+2\right)^2\right)=0\end{cases}}\)
<=> \(\orbr{\begin{cases}x+2=0\\\left(x+2\right)^2=1\end{cases}}\)
<=> \(\orbr{\begin{cases}x+2=0\\x+2=1\end{cases}}\)
<=> \(\orbr{\begin{cases}x=-2\\x=-1\end{cases}}\)