Question

So sánh: A = 10¹⁴ - 1/ 10¹⁵ - 11 và B = 10¹⁴ + 1/ 10¹⁵ + 9

Answer 1

`A=(10^14-1)/(10^15-11)`

`=>10A=(10^15-10)/(10^15-11)`

`=>10A=(10^15-11+1)/(10^15-11)`

`=>10A=1+1/(10^15-1)`

`=>A>1/10`

`B=(10^14+1)/(10^15+9)`

`=>10B=(10^15+10)/(10^15+9)`

`=>10A=(10^15+9+1)/(10^15+9)`

`=>10A=1+1/(10^15+9)`

Vì `1/(10^15-1)>1/(10^15+9)`

`=>10B>10A`

`=>B>A`

Answer 2

Giải:

\(A=\dfrac{10^{14}-1}{10^{15}-11}\) 

\(10A=\dfrac{10^{15}-10}{10^{15}-11}\) 

\(10A=\dfrac{10^{15}-11+1}{10^{15}-11}\) 

\(10A=1+\dfrac{1}{10^{15}-11}\) 

Tương tự:

\(B=\dfrac{10^{14}+1}{10^{15}+9}\) 

\(10B=\dfrac{10^{15}+10}{10^{15}+9}\) 

\(10B=\dfrac{10^{15}+9+1}{10^{15}+9}\) 

\(10B=1+\dfrac{1}{10^{15}+9}\) 

Vì \(\dfrac{1}{10^{15}-11}>\dfrac{1}{10^{15}+9}\) nên \(10A>10B\) 

\(\Rightarrow A>B\) 

Chúc bạn học tốt!