a: \(10A=\dfrac{10^{18}+10}{10^{18}+1}=1+\dfrac{9}{10^{18}+1}\)
\(10B=\dfrac{10^{19}+10}{10^{19}+1}=1+\dfrac{9}{10^{19}+1}\)
\(10^{18}+1< 10^{19}+1\)
=>\(\dfrac{9}{10^{18}+1}>\dfrac{9}{10^{19}+1}\)
=>\(\dfrac{9}{10^{18}+1}+1>\dfrac{9}{10^{19}+1}+1\)
=>10A>10B
=>A>B
b: \(\dfrac{1}{10}A=\dfrac{10^{2012}+1}{10^{2012}+10}=1-\dfrac{9}{10^{2012}+10}\)
\(\dfrac{1}{10}B=\dfrac{10^{2011}+1}{10^{2011}+10}=1-\dfrac{9}{10^{2011}+10}\)
\(10^{2012}+10>10^{2011}+10\)
=>\(\dfrac{9}{10^{2012}+10}< \dfrac{9}{10^{2011}+10}\)
=>\(-\dfrac{9}{10^{2012}+10}>-\dfrac{9}{10^{2011}+10}\)
=>\(-\dfrac{9}{10^{2012}+10}+1>-\dfrac{9}{10^{2011}+10}+1\)
=>1/10A>1/10B
=>A>B
c: \(10A=\dfrac{10^{2013}+10}{10^{2013}+1}=1+\dfrac{9}{10^{2013}+1}\)
\(10B=\dfrac{10^{2014}+10}{10^{2014}+1}=1+\dfrac{9}{10^{2014}+1}\)
\(10^{2013}+1< 10^{2014}+1\)
=>\(\dfrac{9}{10^{2013}+1}>\dfrac{9}{10^{2014}+1}\)
=>\(\dfrac{9}{10^{2013}+1}+1>\dfrac{9}{10^{2014}+1}+1\)
=>10A>10B
=>A>B
d: \(A=\dfrac{10^{12}+6}{10^{12}-11}=\dfrac{10^{12}-11+17}{10^{12}-11}=1+\dfrac{17}{10^{12}-11}\)
\(B=\dfrac{10^{11}+5}{10^{11}-12}=\dfrac{10^{11}-12+17}{10^{11}-12}=1+\dfrac{17}{10^{11}-12}\)
\(10^{12}>10^{11};-11>-12\)
Do đó: \(10^{12}-11>10^{11}-12\)
=>\(\dfrac{17}{10^{12}-11}< \dfrac{17}{10^{11}-12}\)
=>A<B
a) Ta có: \(A=\dfrac{10^{17}+1}{10^{18}+1}\)
\(10A=\dfrac{10^{18}+10}{10^{18}+1}=1+\dfrac{9}{10^{18}+1}\)
Lại có: \(B=\dfrac{10^{18}+1}{10^{19}+1}\)
\(10B=\dfrac{10^{19}+10}{10^{19}+1}=1+\dfrac{9}{10^{19}+1}\)
Ta thấy: \(10^{18}+1< 10^{19}+1\)
\(\Rightarrow\dfrac{1}{10^{18}+1}>\dfrac{1}{10^{19}+1}\)
\(\Rightarrow\dfrac{9}{10^{18}+1}>\dfrac{9}{10^{19}+1}\)
\(\Rightarrow1+\dfrac{9}{10^{18}+1}>1+\dfrac{9}{10^{19}+1}\)
\(\Rightarrow10A>10B\)
hay \(A>B\)
Câu b, c tương tự câu a nhé!
d) Ta có: \(A=\dfrac{10^{12}+6}{10^{12}-11}=\dfrac{10^{12}-11+17}{10^{12}-11}=1+\dfrac{17}{10^{12}-11}\)
\(B=\dfrac{10^{11}+5}{10^{11}-12}=\dfrac{10^{11}-12+17}{10^{11}-12}=1+\dfrac{17}{10^{11}-12}\)
Ta thấy: \(10^{12}>10^{11}\)
\(\Rightarrow10^{12}-11>10^{11}-11>10^{11}-12\)
\(\Rightarrow\dfrac{1}{10^{12}-11}< \dfrac{1}{10^{11}-12}\)
\(\Rightarrow\dfrac{17}{10^{12}-11}< \dfrac{17}{10^{11}-12}\)
\(\Rightarrow1+\dfrac{17}{10^{12}-11}< 1+\dfrac{17}{10^{11}-12}\)
\(\Rightarrow A< B\)
\(\text{#}Toru\)