\(\left(5x-2\right)^{10}=\left(5x-2\right)^{100}\)
\(\Rightarrow\left(5x-2\right)^{100}-\left(5x-2\right)^{10}=0\)
\(\Rightarrow\left(5x-2\right)^{10}\left[\left(5x-2\right)^{90}-1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(5x-2\right)^{10}=0\\\left(5x-2\right)^{90}-1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left(5x-2\right)^{10}=0\\\left(5x-2\right)^{90}=1\Rightarrow5x-2=\pm1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}5x-2=0\Rightarrow5x=2\Rightarrow x=\dfrac{2}{5}\\5x=1;3\Rightarrow x=\dfrac{1}{5};\dfrac{3}{5}\end{matrix}\right.\)
\(\left(\dfrac{2x-3}{4}\right)^{2016}+\left(\dfrac{3y+4}{5}\right)^{2018}=0\)
\(\left\{{}\begin{matrix}\left(\dfrac{2x-3}{4}\right)^{2016}\ge0\forall x\\\left(\dfrac{3y+4}{5}\right)^{2018}\ge0\forall y\end{matrix}\right.\)
\(\Rightarrow\left(\dfrac{2x-3}{4}\right)^{2016}+\left(\dfrac{3y+4}{5}\right)^{2014}\ge0\)
Dấu "=" xảy ra khi:
\(\left\{{}\begin{matrix}\left(\dfrac{2x-3}{4}\right)^{2016}=0\Rightarrow\dfrac{2x-3}{4}=0\Rightarrow2x-3=0\Rightarrow2x=3\Rightarrow x=\dfrac{3}{2}\\\left(\dfrac{3y+4}{5}\right)^{2018}=0\Rightarrow\dfrac{3y+4}{5}=0\Rightarrow3y+4=0\Rightarrow3y=-4\Rightarrow y=\dfrac{-4}{3}\end{matrix}\right.\)
