Question

A,(X-2)^11 = (x-2)^3 ; b, (x-5)^24 = (x-5)^9 ; c, (x-5)^25 = (x-5)^4

Answer 1

a: =>(x-2)^3*[(x-2)^8-1]=0

=>(x-2)(x-3)(x-1)=0

=>\(x\in\left\{2;3;1\right\}\)

b: (x-5)^24=(x-5)^9

=>\(\left(x-5\right)^9\cdot\left[\left(x-5\right)^{15}-1\right]=0\)

=>x-5=0 hoặc x-5=1

=>x=6 hoặc x=5

c: =>(x-5)^4*[(x-5)^21-1]=0

=>x-5=0 hoặc x-5=1

=>x=5 hoặc x=6

Answer 2

a) \(\left(x-2\right)^{11}=\left(x-2\right)^3\)

\(\Rightarrow\left(x-2\right)^{11}-\left(x-2\right)^3=0\)

\(\Rightarrow\left(x-2\right)^3\left[\left(x-2\right)^8-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^3=0\\\left(x-2\right)^8-1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x-2=0\\\left(x-2\right)^8=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x-2=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=3\end{matrix}\right.\)

b) \(\left(x-5\right)^{24}=\left(x-5\right)^9\)

\(\Rightarrow\left(x-5\right)^{24}-\left(x-5\right)^9=0\)

\(\Rightarrow\left(x-5\right)^9\left[\left(x-5\right)^{15}-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-5\right)^9=0\\\left(x-5\right)^{15}-1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^{15}=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=5\\x-5=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)

c) \(\left(x-5\right)^{25}=\left(x-5\right)^4\)

\(\Rightarrow\left(x-5\right)^{25}-\left(x-5\right)^4\)

\(\Rightarrow\left(x-5\right)^4\left[\left(x-5\right)^{21}-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-5\right)^4=0\\\left(x-5\right)^{21}-1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x-5=0\\\left(x-5\right)^{21}=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=5\\x-5=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)