Question

A=10^99+1 / 10^89+1

B= 10^98+1 / 10^88+1

So sánh A và B

Answer 1

Tính chất nếu: 

\(\dfrac{a}{b}>1\Rightarrow\dfrac{a}{b}>\dfrac{a+m}{b+m}\) 

Ta có:

\(A=\dfrac{10^{99}+1}{10^{89}+1}>\dfrac{10^{99}+1+9}{10^{89}+1+9}\)

\(A>\dfrac{10^{99}+10}{10^{89}+10}\)

\(A>\dfrac{10\cdot\left(10^{98}+1\right)}{10\cdot\left(10^{88}+1\right)}\)

\(A>\dfrac{10^{98}+1}{10^{88}+1}\)

\(A>B\)

Answer 2

\(A=\dfrac{10^{99}+1}{10^{89}+1}< \dfrac{10^{99}+1+9}{10^{89}+1+9}=\dfrac{10^{99}+10}{10^{89}+10}=\dfrac{10\left(10^{98}+1\right)}{10\left(10^{88}+1\right)}=\dfrac{10^{98}+1}{10^{88}+1}\)

Vậy \(A< B\)