Question

so sánh không dùng máy tính √2018+√2020 và  2√2019

Answer 1

Ta có \(\left(\sqrt{2018}+\sqrt{2020}\right)^2=4038+2\sqrt{4076360}\) và \(\left(2\sqrt{2019}\right)^2=8076=4038+4038\)

Mà \(\left(2\sqrt{4076360}\right)^2=16305440\) và \(4038^2=16305444\)

\(\Rightarrow2\sqrt{4076360}< 4038\)

\(\Rightarrow\sqrt{2018}+\sqrt{2020}< 2\sqrt{2019}\)

Answer 2

\(\left(\sqrt{2018}+\sqrt{2020}\right)^2=4038+2\cdot\sqrt{2018\cdot2020}\)

\(\left(2\sqrt{2019}\right)^2=8076=4038+4038\)

mà \(2\cdot\sqrt{2018\cdot2020}< 4038\)

nên \(\sqrt{2018}+\sqrt{2020}< 2\sqrt{2019}\)