Đáp án:
`A=1`
Giải thích các bước giải:
Có : `xyz=2021^2`
`⇒` `\sqrt[xyz]=\sqrt[2021^2]=|2021|=2021`
Đặt `A={\sqrt[x]}/{\sqrt[xy]+\sqrt[x]+2021}+{\sqrt[y]}/{\sqrt[yz]+\sqrt[y]+1}+{2021\sqrt[z]}/{\sqrt[xz]+2021\sqrt[z]+2021}`
`A={\sqrt[x]}/{\sqrt[xy]+\sqrt[x]+\sqrt[xyz]}+{\sqrt[y]}/{\sqrt[yz]+\sqrt[y]+1}+{\sqrt[xyz].\sqrt[z]}/{\sqrt[xz]+\sqrt[xyz].\sqrt[z]+2021}`
`A={\sqrt[x]}/{\sqrt[x](\sqrt[y]+1+\sqrt[yz])}+{\sqrt[y]}/{sqrt[yz]+\sqrt[y]+1}+{\sqrt[xz].\sqrt[yz]}/{\sqrt[xz](1+\sqrt[yz]+\sqrt[y])}`
`=1/{\sqrt[y]+1+\sqrt[yz]}+{\sqrt[y]}/{sqrt[yz]+\sqrt[y]+1}+{\sqrt[yz]}/{1+\sqrt[yz]+\sqrt[y]}`
`A=1`
