\( So sánh :{22 \over 29} và {34 \over 41}\)
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\(\frac{22}{29}=1-\frac{7}{29}\)
\(\frac{34}{41}=1-\frac{7}{41}\)
\(\frac{7}{29}\)>\(\frac{7}{41}\Rightarrow\frac{22}{29}\)<\(\frac{34}{41}\)
Ta có: \(\frac{22}{29}< \frac{22}{28}=\frac{11}{14}=\frac{33}{42}< \frac{34}{42}< \frac{34}{41}\)
Vậy \(\frac{22}{29}< \frac{34}{41}\)
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Ta thấy :
\(\frac{20}{39}>\frac{14}{39}\)
\(\frac{22}{27}>\frac{22}{29}\)
\(\frac{18}{43}< \frac{18}{41}\)
\(\Rightarrow\frac{20}{39}+\frac{22}{27}+\frac{18}{43}>\frac{14}{39}+\frac{22}{29}+\frac{18}{41}\)
=> A > B
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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
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![](https://rs.olm.vn/images/avt/0.png?1311)
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Áp dụng bất đẳng thức : \(\frac{a}{b}< 1\Rightarrow\frac{a}{b}< \frac{a+n}{b+n}\)
Ta chứng minh được \(\frac{20}{39}>\frac{18}{41};\frac{18}{43}>\frac{14}{39};\frac{22}{27}>\frac{22}{29}\)
\(\Rightarrow\frac{20}{39}+\frac{22}{27}+\frac{18}{43}>\frac{14}{37}+\frac{22}{29}+\frac{18}{41}\)
\(\Rightarrow A>B\)
Ta có: \(22\frac{2}{9}=\frac{200}{9}\)
\(34\frac{4}{1}=38=\frac{342}{9}\)
Vì \(\frac{200}{9}< \frac{342}{9}\)nên \(22\frac{2}{9}< 34\frac{4}{1}\)
Vậy \(22\frac{2}{9}< 34\frac{4}{1}\)