a) \(\left(3x\right)^6=\left(3x\right)^7\)
\(\Rightarrow\left(3x\right)^6-\left(3x\right)^7=0\)
\(\Rightarrow\left(3x\right)^6\left(1-3x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}\left(3x\right)^6=0\\1-3x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{1}{3}\end{matrix}\right.\)
b) \(\left(\dfrac{2}{5}x\right)^{2020}+\left(\dfrac{3}{7}+y\right)^{2022}\le0\)
Vì \(\left\{{}\begin{matrix}\left(\dfrac{2}{5}x\right)^{2020}\ge0\\\left(y+\dfrac{3}{7}\right)^{2022}\ge0\end{matrix}\right.\)
với mọi x,y
\(\Rightarrow\left(\dfrac{2}{5}x\right)^{2020}+\left(y+\dfrac{3}{7}\right)^{2022}\ge0\)
mà \(\left(\dfrac{2}{5}x\right)^{2020}+\left(y+\dfrac{3}{7}\right)^{2022}\le0\)
\(\Rightarrow\left(\dfrac{2}{5}x\right)^{2020}+\left(y+\dfrac{3}{7}\right)^{2022}=0\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{2}{5}x=0\\y+\dfrac{3}{7}=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\y=-\dfrac{3}{7}\end{matrix}\right.\)
