Question

giúp mk câu c và câu b nhá!!!!!

Answer 1

a) Ta có: \(\sqrt{2018}-\sqrt{2017}=\dfrac{1}{\sqrt{2018}+\sqrt{2017}}\)

\(\sqrt{2016}-\sqrt{2015}=\dfrac{1}{\sqrt{2016}+\sqrt{2015}}\)

mà \(\dfrac{1}{\sqrt{2018}+\sqrt{2017}}< \dfrac{1}{\sqrt{2016}+\sqrt{2015}}\)

nên \(\sqrt{2018}-\sqrt{2017}< \sqrt{2016}-\sqrt{2015}\)

b) Ta có: \(\left(\sqrt{2018}+\sqrt{2016}\right)^2=4034+24\sqrt{14126}\)

\(\left(2\sqrt{2017}\right)^2=8068=4034+4034\)

mà \(24\sqrt{14126}< 4034\)

nên \(\sqrt{2018}+\sqrt{2016}< 2\sqrt{2017}\)