\(\left(x+1\right)^{2020}+\left(2-3y\right)^{2022}=0\)
Vì \(\hept{\begin{cases}\left(x+1\right)^{2020}\ge0\forall x\\\left(2-3y\right)^{2022}\ge0\forall y\end{cases}}\Rightarrow\left(x+1\right)^{2020}+\left(2-3y\right)^{2022}\ge0\forall x,y\)
Dấu " = " xảy ra khi và chỉ khi \(\hept{\begin{cases}\left(x+1\right)^{2020}=0\\\left(2-3y\right)^{2022}=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-1\\3y=2\end{cases}}\Rightarrow\hept{\begin{cases}x=-1\\y=\frac{2}{3}\end{cases}}\)
( x + 1 )2020 + ( 2 - 3y )2022 = 0
Ta có \(\hept{\begin{cases}\left(x+1\right)^{2020}\ge0\forall x\\\left(2-3y\right)^{2022}\ge0\forall y\end{cases}}\Rightarrow\left(x+1\right)^{2020}+\left(2-3y\right)^{2022}\ge0\forall x,y\)
Đẳng thức xảy ra <=> \(\hept{\begin{cases}x+1=0\\2-3y=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-1\\y=\frac{2}{3}\end{cases}}\)
Vậy x = -1 ; y = 2/3
