Question

1. So sánh

a) A=\(\dfrac{10^{15}.11}{10^{16}+1}\) với B=\(\dfrac{10^{16}+10}{10^{16}+1}\)

b) C+\(\dfrac{10^{10}+1}{10^{10}-1}\) với D=\(\dfrac{10^{10}-1}{10^{13}-3}\)

Answer 1

a, Ta có : \(10^{15}\cdot11=10^{15}\left(10+1\right)=10^{16}+10^{15}\)

Vì \(10^{16}+10^{15}>10^{16}+10\)

\(\Rightarrow\dfrac{10^{16}+10^{15}}{10^{16}+1}>\dfrac{10^{16}+10}{10^{16}+1}\)

Hay A>B

b, Ta có : \(C=\dfrac{10^{10}+1}{10^{10}-1}=\dfrac{10^{10}}{10^{10}-1}+\dfrac{1}{10^{10}-1}\)

\(D=\dfrac{10^{10}-1}{10^{13}-3}=\dfrac{10^{10}}{10^{13}-3}+\dfrac{-1}{10^{13}-3}\)

Vì \(\dfrac{10^{10}}{10^{10}-1}>\dfrac{10^{10}}{10^{13}-3};\dfrac{1}{10^{10}-1}>\dfrac{-1}{10^{13}-3}\)

\(\Rightarrow\dfrac{10^{10}+1}{10^{10}-1}>\dfrac{10^{10}-1}{10^{13}-3}\)

Hay C > D

Answer 2

a, Ta có : \(1 0^{15} \cdot 11 = 1 0^{15} \left(\right. 10 + 1 \left.\right) = 1 0^{16} + 1 0^{15}\)

Vì \(1 0^{16} + 1 0^{15} > 1 0^{16} + 10\)

\(\Rightarrow \frac{1 0^{16} + 1 0^{15}}{1 0^{16} + 1} > \frac{1 0^{16} + 10}{1 0^{16} + 1}\)

Hay A>B

b, Ta có : \(C = \frac{1 0^{10} + 1}{1 0^{10} - 1} = \frac{1 0^{10}}{1 0^{10} - 1} + \frac{1}{1 0^{10} - 1}\)

\(D = \frac{1 0^{10} - 1}{1 0^{13} - 3} = \frac{1 0^{10}}{1 0^{13} - 3} + \frac{- 1}{1 0^{13} - 3}\)

Vì \(\frac{1 0^{10}}{1 0^{10} - 1} > \frac{1 0^{10}}{1 0^{13} - 3} ; \frac{1}{1 0^{10} - 1} > \frac{- 1}{1 0^{13} - 3}\)

\(\Rightarrow \frac{1 0^{10} + 1}{1 0^{10} - 1} > \frac{1 0^{10} - 1}{1 0^{13} - 3}\)

Hay C > D