Bài 16:
\(10A=\dfrac{10^{20}+10}{10^{20}+1}=1+\dfrac{9}{10^{20}+1}\)
\(10B=\dfrac{10^{21}+10}{10^{21}+1}=1+\dfrac{9}{10^{21}+1}\)
Vì \(10^{20}+1< 10^{21}+1\)
nên \(\dfrac{9}{10^{20}+1}>\dfrac{9}{10^{21}+1}\)
=>\(1+\dfrac{9}{10^{20}+1}>1+\dfrac{9}{10^{21}+1}\)
=>10A>10B
=>A>B
Câu 15:
\(A=\dfrac{100^{10}+1}{100^{10}-1}=\dfrac{100^{10}-1+2}{100^{10}-1}=1+\dfrac{2}{100^{10}-1}\)
\(B=\dfrac{100^{10}-1}{100^{10}-3}=\dfrac{100^{10}-3+2}{100^{10}-3}=1+\dfrac{2}{100^{10}-3}\)
Vì \(100^{10}-1>100^{10}-3\)
nên \(\dfrac{2}{100^{10}-1}< \dfrac{2}{100^{10}-3}\)
=>\(1+\dfrac{2}{100^{10}-1}< 1+\dfrac{2}{100^{10}-3}\)
=>A<B
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