So sánh: \(\frac{2016}{\sqrt{2015}}+\frac{2015}{\sqrt{2016}}\text{ và }\sqrt{2015}+\sqrt{2016}\)(không dùng máy tính cầm tay)
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5 tháng 10 2021
b: \(\sqrt{2017}-\sqrt{2016}=\dfrac{1}{\sqrt{2016}+\sqrt{2017}}\)
\(\sqrt{2016}-\sqrt{2015}=\dfrac{1}{\sqrt{2016}+\sqrt{2015}}\)
mà \(\sqrt{2016}+\sqrt{2017}< \sqrt{2016}+\sqrt{2015}\)
nên \(\sqrt{2017}-\sqrt{2016}>\sqrt{2016}-\sqrt{2015}\)
10 tháng 9 2023
\(\sqrt{2017}-\sqrt{2016}=\dfrac{1}{\sqrt{2017}+\sqrt{2016}}\)
\(\sqrt{2016}-\sqrt{2015}=\dfrac{1}{\sqrt{2016}+\sqrt{2015}}\)
2017>2015
=>căn 2017>căn 2015
=>\(\sqrt{2017}+\sqrt{2016}>\sqrt{2016}+\sqrt{2015}\)
=>\(\dfrac{1}{\sqrt{2017}+\sqrt{2016}}< \dfrac{1}{\sqrt{2016}+\sqrt{2015}}\)
=>\(\sqrt{2017}-\sqrt{2016}< \sqrt{2016}-\sqrt{2015}\)
QA
1
21 tháng 10 2016
Có: \(\sqrt{2015}< \sqrt{2016}\)
=>\(\frac{1}{\sqrt{2015}}>\frac{1}{\sqrt{2016}}\)
=>\(\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}>0\)
=>\(\sqrt{2015}+\sqrt{2016}+\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}>\sqrt{2015}+\sqrt{2016}\)
=>\(\left(\sqrt{2015}+\frac{1}{\sqrt{2015}}\right)+\left(\sqrt{2016}-\frac{1}{\sqrt{2016}}\right)>\sqrt{2015}+\sqrt{2016}\)
=>\(\frac{2016}{\sqrt{2015}}+\frac{2015}{\sqrt{2016}}>\sqrt{2015}+\sqrt{2016}\)
PQ
0
VT
30 tháng 9 2019
a)1/7\(\sqrt{51}\)=\(\sqrt{\frac{51}{49}}\);1/9\(\sqrt{150}=\sqrt{\frac{150}{81}}=\sqrt{\frac{50}{27}}\)
\(\frac{51}{49}=1+\frac{1}{49}+\frac{1}{49}\);\(\frac{50}{27}=1+\frac{23}{27}>1+\frac{23}{36}>\)\(1+\frac{2}{36}=1+\frac{1}{36}+\frac{1}{36}\)
1/49<1/36 nên 51/49<50/27 =>1/7\(\sqrt{51}\)<1/9\(\sqrt{150}\)
b) \(\sqrt{2017}+\sqrt{2016}>\sqrt{2016}\)+\(\sqrt{2015}\)
=>\(\frac{1}{\sqrt{2017}+\sqrt{2016}}< \)\(\frac{1}{\sqrt{2016}+\sqrt{ }2015}\) <=> \(\sqrt{2017}-\sqrt{2016}< \sqrt{2016}\)-\(\sqrt{2015}\)
TT
1
5 tháng 2 2022
\(\sqrt{2016}-\sqrt{2015}=\dfrac{1}{\sqrt{2016}+\sqrt{2015}}\)
\(\sqrt{2015}-\sqrt{2014}=\dfrac{1}{\sqrt{2015}+\sqrt{2014}}\)
mà \(\sqrt{2016}+\sqrt{2015}>\sqrt{2014}+\sqrt{2015}\)
nên \(\sqrt{2016}-\sqrt{2015}< \sqrt{2015}-\sqrt{2014}\)
TA
1
15 tháng 6 2018
\(\frac{2016}{\sqrt{2016}}=\sqrt{2016}\)
\(\frac{2017}{\sqrt{2017}}=\sqrt{2017}\)
=> Bằng nhau
16 tháng 6 2018
\(\frac{2016}{\sqrt{2017}}+\frac{2017}{\sqrt{2016}}-\sqrt{2016}-\sqrt{2017}=\left(\frac{2016}{\sqrt{2017}}-\sqrt{2017}\right)+\left(\frac{2017}{\sqrt{2016}}-\sqrt{2016}\right)\)
\(=\frac{2016-2017}{\sqrt{2017}}+\frac{2017-2016}{\sqrt{2016}}=\frac{1}{\sqrt{2016}}-\frac{1}{\sqrt{2017}}\)
vì \(2016< 2017\Rightarrow\sqrt{2016}< \sqrt{2017}\Rightarrow\frac{1}{\sqrt{2016}}>\frac{1}{\sqrt{2017}}\Rightarrow\frac{1}{\sqrt{2016}}-\frac{1}{\sqrt{2017}}>0\)
\(\Rightarrow\frac{2016}{\sqrt{2017}}+\frac{2017}{\sqrt{2016}}-\sqrt{2016}-\sqrt{2017}>0\Rightarrow\frac{2016}{\sqrt{2017}}+\frac{2017}{\sqrt{2016}}>\sqrt{2016}+\sqrt{2017}\)
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