Question

So sánh A và 4 :

\(A=\frac{18}{11}+\frac{11}{13}+\frac{15}{17}+\frac{17}{15}\)

Cũng cần gấp trước thứ Tư tuần sau !

Answer 1

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Answer 2

\(A=\frac{18}{11}+\frac{11}{13}+\frac{15}{17}+\frac{17}{15}\)

\(=1+\frac{7}{11}+1-\frac{2}{13}+1-\frac{2}{17}+1+\frac{2}{15}\)

\(=4+\frac{7}{11}+\frac{2}{15}-\frac{2}{13}-\frac{2}{17}\)

\(\frac{7}{11}>\frac{2}{11}>\frac{2}{13};\frac{2}{15}>\frac{2}{17}\Rightarrow\frac{7}{11}+\frac{2}{15}>\frac{2}{11}+\frac{2}{17}\)

\(\Rightarrow\frac{7}{11}+\frac{2}{15}-\frac{2}{13}-\frac{2}{17}>0\)

\(\Rightarrow A>4+0=4\)

Vậy A>4

Answer 3

Vì 11/13 > 11/18 nên dễ thấy A > 18/11 + 11/18 + 15/17 + 17/15.

Mặc khác, 18/11 + 11/18 + 15/17 + 17/15 = 1 + 7/11 + 1 - 7/18 + 1 - 2/17 + 1 + 2/15

              = 4 + 7/11-7/18+2/15-2/17 > 4 (Vì 7/11 > 7/18, 2/15 > 2/17)

Vậy A > 4

Answer 4

\(A=\frac{18}{11}+\frac{11}{13}+\frac{15}{17}+\frac{17}{15}\)

\(=1+\frac{7}{11}+1-\frac{2}{13}+1-\frac{2}{17}+1+\frac{2}{15}\)

\(=4+\frac{7}{11}+\frac{2}{15}-\frac{2}{13}-\frac{2}{17}\)

\(\frac{7}{11}>\frac{2}{11}>\frac{2}{13};\frac{2}{15}>\frac{2}{17}\Rightarrow\frac{7}{11}+\frac{2}{15}>\frac{2}{11}+\frac{2}{17}\)

\(\Rightarrow\frac{7}{11}+\frac{2}{15}-\frac{2}{13}-\frac{2}{17}>0\)

\(\Rightarrow A>4+0=4\)

Vậy A > 4