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-2012/4025>-1999/3997

Ta có -2012/4025 < -2012/4024 tức là < -1/2

Ta có -1999/3997 > -1999/3998 tức là > -1/2 

=> -1999/3997 >  -2012/4025

Ta có 3^21 = 3^(2.10 + 1) = 9^ 10 .3 

Ta có 2^31= 2^( 3.10+1) = 8^10.2

Từ đó => 3^21 > 2^31

a) Ta có: \(\frac{2012}{4025}< \frac{2012}{4024}=\frac{1}{2}\)

mà \(\frac{1999}{3997}>\frac{1999}{3998}=\frac{1}{2}\)

\(\Rightarrow\frac{2012}{4025}< \frac{1999}{3997}\)\(\Rightarrow\frac{-2012}{4025}>\frac{-1999}{3997}\)\(\Rightarrow A>B\)

b) \(A=3^{21}=3^{20+1}=3^{20}.3=3^{2.10}.3=9^{10}.3\)

\(B=2^{31}=2^{30+1}=2^{30}.2=2^{3.10}.2=8^{10}.2\)

Vì \(9>8\)\(\Rightarrow9^{10}>8^{10}\)

mà \(3>2\)\(\Rightarrow9^{10}.3>8^{10}.2\)\(\Rightarrow3^{21}>2^{31}\)\(\Rightarrow A>B\)

Ta có:

\(A=\frac{-2012}{4025}=\frac{-2012}{4025}.2=\frac{-4024}{4025}\)

\(B=\frac{-1999}{3997}=\frac{-1999}{3997}.2=\frac{-3998}{3997}\)

\(\frac{4024}{4025}< 1< \frac{3998}{3997}\Rightarrow\frac{4024}{4025}< \frac{3998}{3887}\Rightarrow\frac{-4024}{4025}>\frac{-3998}{3997}\)hay \(\frac{-2012}{4025}>\frac{-1999}{3997}\)

\(\Rightarrow A>B\)

\(A=\dfrac{-2012}{4025}< 0\)

\(B=\dfrac{1999}{3997}>0\)

\(\Rightarrow A< B\)

Ta có:

A=-2012/4025=>-2012/4025x2=-4024/4025

B=-1999/3997=>-1999/3997x2=-3998/3997

Ta có: 4024/4025<1<3998/3997

=>4024/4025<3998/3997

=>-4024/4025>-3998/3997

=>-2012/4025>-1999/3997

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