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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(\dfrac{20}{39}>\dfrac{20}{41}>\dfrac{18}{41}\left(1\right)\)
\(\dfrac{22}{27}>\dfrac{22}{29}\left(2\right)\)
\(\dfrac{18}{43}=1-\dfrac{25}{43};\dfrac{14}{39}=1-\dfrac{25}{39}\)
Vì \(\dfrac{25}{43}< \dfrac{25}{39}\Rightarrow1-\dfrac{25}{43}>1-\dfrac{25}{39}\Rightarrow\dfrac{18}{43}>\dfrac{14}{39}\left(3\right)\)
Từ \(\left(1\right);\left(2\right);\left(3\right)\) ta suy ra : A>B
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có 20/39 > 14/39
22/27 > 22/29
18/43 < 18/41
=> 20/39+22/27+18/43 > 14/39+22/29+18/41
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
xét A và B, ta thấy:
20/39>14/39
22/27>22/29
18/43<18/41
Ta có: 20/39+22/27>14/39+22/29
2012^2013+2013^2013<2013^2013+2013^2014
![](https://rs.olm.vn/images/avt/0.png?1311)
Áp dụng bất đẳng thức : \(\frac{a}{b}< 1\Rightarrow\frac{a}{b}< \frac{a+n}{b+n}\)
Ta chứng minh được \(\frac{20}{39}>\frac{18}{41};\frac{18}{43}>\frac{14}{39};\frac{22}{27}>\frac{22}{29}\)
\(\Rightarrow\frac{20}{39}+\frac{22}{27}+\frac{18}{43}>\frac{14}{37}+\frac{22}{29}+\frac{18}{41}\)
\(\Rightarrow A>B\)
xét A và B,ta thấy:
20/39>14/39
22/27>22/29
18/43<18/41
Ta có: 20/39+22/27>14/39+22/29
2012^2013+2013^2013<2013^2013+2013^2014
xet A va B ta thay:
20/39>14/39
22/27>22/29
18/43<18/41
vay A>B