Question

So sánh A và B​

​A=8^9+12/8^9+7

B=8^10+4/8^10-1 Bạn nào làm nhanh và đúng mình cho 1 tick

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Answer 1

\(\dfrac{8^9+12}{8^9+7}=\dfrac{8^9+7+5}{8^9+7}=1+\dfrac{5}{8^9+7}\)

\(\dfrac{8^{10}+4}{8^{10}-1}=\dfrac{8^{10}-1+5}{8^{10}-1}=1+\dfrac{5}{8^{10}-1}\)

Vì \(8^{10}-1>8^9+7\)

\(\Rightarrow\dfrac{5}{8^{10}-1}< \dfrac{5}{8^9+7}\)

\(\Rightarrow\)\(1+\dfrac{5}{8^{10}-1}< 1+\dfrac{5}{8^9+7}\)

\(\Rightarrow\) A < B

Answer 2

\(A=\dfrac{8^9+12}{8^9+7}=\dfrac{8^9+7+5}{8^9+7}=\dfrac{8^9+7}{8^9+7}+\dfrac{5}{8^9+7}=1+\dfrac{5}{8^9+7}\\ B=\dfrac{8^{10}+4}{8^{10}-1}=\dfrac{8^{10}-1+5}{8^{10}-1}=\dfrac{8^{10}-1}{8^{10}-1}+\dfrac{5}{8^{10}-1}=1+\dfrac{5}{8^{10}-1}\\ \dfrac{5}{8^9+7}>\dfrac{5}{8^{10}-1}\Rightarrow1+\dfrac{5}{8^9+7}>1+\dfrac{5}{8^{10}-1}\Rightarrow A>B\)

Answer 3

A<B