Question

[Vũ Thảo Vy]

So sánh không dùng máy tính bỏ túi : \(\sqrt{2018}\)+\(\sqrt{2020}\)và 2\(\sqrt{2019}\)

Answer 1

[Nguyễn Xuân Anh]

Đặt \(A=\left(\sqrt{2018}+\sqrt{2020}\right)\)

\(\Rightarrow A^2=2018+2\sqrt{2018.2020}+2020=4038+\sqrt{4.2018.2020}=4038+\sqrt{4.\left(2019^2-1\right)}\)

Đặt \(B=2\sqrt{2019}=\sqrt{4.2019}\)

\(B^2=4.2019=2.2019+2.2019=4038+\sqrt{4.2019^2}\)

=> \(\sqrt{4.2019^2}>\sqrt{4.\left(2019^2-1\right)}\)

\(\Rightarrow A>B\Leftrightarrow\sqrt{2018}+\sqrt{2020}>2\sqrt{2019}\)