\(a,\left(y^{54}\right)^2=y\)\(\Rightarrow y^{108}=y\)\(\Rightarrow y=\pm1\)
\(b,\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)
\(\Rightarrow\left(x-1\right)^{x+4}-\left(x-1\right)^{x+2}=0\)
\(\Rightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\)
\(\Rightarrow x\left(x-1\right)^{x+2}\left(x-2\right)=0\)
\(\Rightarrow x\in\left\{0;1;2\right\}\)
\(c,x\left(6-x\right)^{2019}=\left(6-x\right)^{2019}\)
\(\Rightarrow\left(6-x\right)^{2019}\left(x-1\right)=0\)
\(\Rightarrow x\in\left\{1;6\right\}\)
\(\left(y^{54}\right)^2=y\)
\(\Rightarrow y^{108}=y\)
\(\Rightarrow y^{108}-y=0\)
\(\Rightarrow y\cdot\left(y^{107}-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}y=0\\y^{107}-1=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}y=0\\y^{107}=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}y=0\\y=1\end{cases}}\)
a) \(\left(y^{54}\right)^2=y\)
\(\Leftrightarrow y^{108}=y\)
\(\Leftrightarrow y^{108}-y=0\)
\(\Leftrightarrow y.\left(y^{107}-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}y=0\\y^{107}-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}y=0\\y=1\end{cases}}}\)
Vậy \(y\in\left\{0;1\right\}\)
\(\left(\times-1\right)^{\times+2}=\left(\times-1\right)^{\times+4}\)
\(\Rightarrow\left(\times-1\right)^{\times+4}-\left(\times-1\right)^{\times+2}=0\)
\(\Rightarrow\left(\times-1\right)^{\times+2}\cdot\left[\left(\times-1\right)^{\times+2}-1\right]=0\)
\(\Rightarrow\hept{\begin{cases}\left(\times-1\right)^{\times+2}=0\\\left(\times-1\right)^{\times+2}=1\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}\times-1=0;\times\inℚ\\\orbr{\begin{cases}\times-1=1;\times\inℚ\\\times+2=0;\times\inℚ\end{cases}}\end{cases}}\)
\(\Rightarrow\hept{\begin{cases}\times=1\\\times=2\\\times=-2\end{cases}}\)
b)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)
\(\left(x-1\right)^{x+2}-\left(x-1\right)^{x+4}=0\)
\(\left(x-1\right)^{x+2}\left[1-\left(x-1\right)^2\right]=0\)
\(\left(x-1\right)^2.x.\left(-x+2\right)=0\)
\(\Rightarrow x=1;x=0;x=2\)
Vậy \(x\in\left\{1;0;2\right\}\)
