Question

So sánh:

\(\dfrac{10^{2016}+2}{10^{2016}-1};\dfrac{10^{2016}}{10^{2016}}-3\)

Answer 1

\(\dfrac{10^{2016}+2}{10^{2016}-1}=\dfrac{10^{2016}-1+3}{10^{2016}-1}=1+\dfrac{3}{10^{2016}-1}>0\)

\(\dfrac{10^{2016}}{10^{2016}}-3=1-3=-2< 0\)

\(\Rightarrow\dfrac{10^{2016}+2}{10^{2016}-1}>\dfrac{10^{2016}}{10^{2016}}-3\)

Answer 2

Hình như bạn viết đề sai:

Sửa đề:

Đặt:

\(A=\dfrac{2^{2016}+2}{2^{2016}-1};B=\dfrac{2^{2016}}{2^{2016}-3}\)

Ta có : Nếu:

\(\dfrac{a}{b}>1\Leftrightarrow\dfrac{a+m}{b+m}>1\left(m\in N\right)\)

Mà:

\(B=\dfrac{2^{2016}}{2^{2016}-3}>1\)

\(\Leftrightarrow\dfrac{2^{2016}}{2^{2016}-3}>\dfrac{2^{2016}+2}{2^{2016}-3+2}>\dfrac{2^{2016}+2}{2^{2016}-1}=A\)

Answer 3

\(\dfrac{10^{2016}+2}{10^{2016}+1}=\dfrac{10^{2016}+1+1}{10^{2016}+1}=1+\dfrac{1}{10^{2016}+1}\)

\(\dfrac{10^{2016}}{10^{2016}-3}=\dfrac{10^{2016}-3+3}{10^{2016}-3}=1+\dfrac{3}{10^{2016}-3}\)

Vì \(\dfrac{1}{10^{2016}+1}< \dfrac{3}{10^{2016}-3}\Rightarrow\dfrac{10^{2016}+2}{10^{2016}+1}< \dfrac{10^{2016}}{10^{2016}-3}\)

Chỗ nào ko hiểu thì hỏi