Ta có: \(A=\frac{2021}{\sqrt{2022}}+\frac{2022}{\sqrt{2021}}\)
\(=\frac{2021\cdot\sqrt{2021}+2022\cdot\sqrt{2022}}{\sqrt{2022\cdot2021}}=\frac{\left(\sqrt{2021}\right)^3+\left(\sqrt{2022}^{}\right)^3}{\sqrt{2022\cdot2021}}\)
\(=\left(\sqrt{2021}+\sqrt{2022}\right)\left(\frac{2021-\sqrt{2021\cdot2022}+2022}{\sqrt{2022\cdot2021}}\right)=B\cdot\left(\frac{4043}{\sqrt{2022\cdot2021}}-1\right)\)
=>A>B
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