so sánh căn 2017 cộng căn 2020 và căn 2018 cộng căn 2019 09/08/2021 Bởi aihong so sánh căn 2017 cộng căn 2020 và căn 2018 cộng căn 2019
Xét (√2018+√2019)² =2018+2019+2√2018.2019 =4037+2√2018.2019(1) Xét (√2017+√2020)² =2017+2020+2√2017.2020 =4037+2√2017.2020(2) Lại có 2018.2019=2018.(2017+2)=2018.2017+2018.2 2017.2020=2017.(2018+2)=2017.2018+2017.2 ⇒2018.2019>2017.2020(3) Từ (1),(2),(3) ⇒√2018+√2019>√2017+√2020 Xin câu trả lời hay nhất Bình luận
Ta có: $(\sqrt[]{2017}+\sqrt[]{2020})^2$ $=2017+2020+2\sqrt[]{2017.2020}$ $=4037+2\sqrt[]{2017.(2018+2)}$ $=4037+2\sqrt[]{2017.2018+2017.2}$ $(\sqrt[]{2018}+\sqrt[]{2019})^2$ $=2018+2019+2\sqrt[]{2018.2019}$ $=4037+2\sqrt[]{2018.(2017+2)}$ $=4037+2\sqrt[]{2018.2017+2018.2}$ Vì $(\sqrt[]{2017}+\sqrt[]{2020})>0$, $(\sqrt[]{2018}+\sqrt[]{2019})>0$ và $(2017.2018+2017.2)<(2018.2017+2018.2)$ nên $\sqrt[]{2017}+\sqrt[]{2020}<\sqrt[]{2018}+\sqrt[]{2019}$. Bình luận
Xét
(√2018+√2019)²
=2018+2019+2√2018.2019
=4037+2√2018.2019(1)
Xét
(√2017+√2020)²
=2017+2020+2√2017.2020
=4037+2√2017.2020(2)
Lại có 2018.2019=2018.(2017+2)=2018.2017+2018.2
2017.2020=2017.(2018+2)=2017.2018+2017.2
⇒2018.2019>2017.2020(3)
Từ (1),(2),(3) ⇒√2018+√2019>√2017+√2020
Xin câu trả lời hay nhất
Ta có:
$(\sqrt[]{2017}+\sqrt[]{2020})^2$
$=2017+2020+2\sqrt[]{2017.2020}$
$=4037+2\sqrt[]{2017.(2018+2)}$
$=4037+2\sqrt[]{2017.2018+2017.2}$
$(\sqrt[]{2018}+\sqrt[]{2019})^2$
$=2018+2019+2\sqrt[]{2018.2019}$
$=4037+2\sqrt[]{2018.(2017+2)}$
$=4037+2\sqrt[]{2018.2017+2018.2}$
Vì $(\sqrt[]{2017}+\sqrt[]{2020})>0$, $(\sqrt[]{2018}+\sqrt[]{2019})>0$ và $(2017.2018+2017.2)<(2018.2017+2018.2)$ nên $\sqrt[]{2017}+\sqrt[]{2020}<\sqrt[]{2018}+\sqrt[]{2019}$.