Question

A= 10⁸ + 1 /10⁹ + 1 và B = 10⁹ + 1/ 10¹⁰ + 1 Hãy so sánh A và B

Answer 1

\(taco\)

\(A=\frac{10^8+1}{10^9+1}\Rightarrow10A=1+\frac{9}{10^9+1}\)

\(B=\frac{10^9+1}{10^{10}+1}\Rightarrow10B=1+\frac{9}{10^{10}+1}\)

\(Vì:\frac{9}{10^9+1}>\frac{9}{10^{10}+1}\Rightarrow10A>10B\Rightarrow A>B\)

Answer 2

Ta có:

\(A=\frac{10^8+1}{10^9+1}\Leftrightarrow10A=\frac{10^9+10}{10^9+1}=\frac{10^9+1+9}{10^9+1}=1+\frac{9}{10^9+1}\)

\(B=\frac{10^9+1}{10^{10}+1}\Leftrightarrow10B=\frac{10^{10}+10}{10^{10}+1}=\frac{10^{10}+1+9}{10^{10}+1}=1+\frac{9}{10^{10}+1}\)

Vì \(\frac{9}{10^9+1}>\frac{9}{10^{10}+1}\)nên \(1+\frac{9}{10^9+1}>1+\frac{9}{10^{10}+1}\)

\(\Rightarrow10A>10B\)\(\Rightarrow A>B\)

Vậy A>B