Question

[Roxie]

Tim x,biet

a)(x-6)¹⁰=(x-6)⁸

Answer 1

[Vũ Minh Tuấn]

a) \(\left(x-6\right)^{10}=\left(x-6\right)^8\)

\(\Rightarrow\left(x-6\right)^{10}-\left(x-6\right)^8=0\)

\(\Rightarrow\left(x-6\right)^8.\left[\left(x-6\right)^2-1\right]=0\)

\(\Rightarrow\left[{}\begin{matrix}\left(x-6\right)^8=0\\\left(x-6\right)^2-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x-6=0\\\left(x-6\right)^2=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=0+6\\x-6=\pm1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=6\\x-6=1\\x-6=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=6\\x=7\\x=5\end{matrix}\right.\)

Vậy \(x\in\left\{6;7;5\right\}.\)

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