Question

Cho A= \(\frac{5^{60}+1}{5^{61}+1}\)và B= \(\frac{5^{61}+1}{5^{62}+1}\). Hãy so sánh A và B

Answer 1

* Cách 1 : 

Ta có : 

\(5A=\frac{5^{61}+5}{5^{61}+1}=\frac{5^{61}+1+4}{5^{61}+1}=\frac{5^{61}+1}{5^{61}+1}+\frac{4}{5^{61}+1}=1+\frac{4}{5^{61}+1}\)

\(5B=\frac{5^{62}+5}{5^{62}+1}=\frac{5^{62}+1+4}{5^{62}+1}=\frac{5^{62}+1}{5^{62}+1}+\frac{4}{5^{62}+1}=1+\frac{4}{5^{62}+1}\)

Vì \(\frac{4}{5^{61}+1}>\frac{4}{5^{62}+1}\) nên \(1+\frac{4}{5^{61}+1}>1+\frac{4}{5^{62}+1}\) 

\(\Rightarrow\)\(5A>5B\) hay \(A>B\)

Vậy \(A>B\)

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