cứu em ạaaa
Đặt \(x=a^{2011};y=b^{2011};z=c^{2011}\)
\(a^{2022}+b^{2022}+c^{2022}=a^{1011}\cdot b^{1011}+b^{1011}\cdot c^{1011}+c^{1011}\cdot a^{1011}\)
=>\(x^2+y^2+z^2=xy+yz+xz\)
=>\(2x^2+2y^2+2z^2-2xy-2yz-2xz=0\)
=>\(\left(x^2-2xy+y^2\right)+\left(y^2-2yz+z^2\right)+\left(x^2-2xz+z^2\right)=0\)
=>\(\left(x-y\right)^2+\left(y-z\right)^2+\left(x-z\right)^2=0\)
=>\(\left\{{}\begin{matrix}x-y=0\\y-z=0\\x-z=0\end{matrix}\right.\)
=>x=y=z
=>\(a^{2011}=b^{2011}=c^{2011}\)
=>a=b=c
\(A=\left(a-b\right)^{2020}+\left(b-c\right)^{2021}+\left(a-c\right)^{2022}\)
\(=\left(a-a\right)^{2020}+\left(b-b\right)^{2021}+\left(c-c\right)^{2022}\)
=0+0+0
=0
