Question

So sánh:

\(A=\frac{3^{10}+1}{3^9+1}vàB=\frac{3^9+1}{3^8+1}\)

Answer 1

\(\frac{A}{3}=\frac{3^{10}+1}{3^{10}+3}=\frac{\left(3^{10}+3\right)-2}{3^{10}+3}=1-\frac{2}{3^{10}+3}\)

\(\frac{B}{3}=\frac{3^9+1}{3^9+3}=\frac{\left(3^9+3\right)-2}{3^9+3}=1-\frac{2}{3^9+3}\)

Vì \(3^{10}+3>3^9+3\) nên \(\frac{2}{3^{10}+3}< \frac{2}{3^9+3}\) \(\Leftrightarrow1-\frac{2}{3^{10}+3}>1-\frac{2}{3^9+3}\)

\(\Rightarrow\frac{A}{3}>\frac{B}{3}\) Hay \(A>B\)

Answer 2

Ta có:

\(A=\frac{3^{10}+1}{3^9+1}>\frac{3^{10}+3}{3^9+3}=\frac{3\left(3^9+1\right)}{3\left(3^8+1\right)}=\)\(\frac{3^9+1}{3^8+1}=B\Rightarrow A>B\)

Answer 3

\(A=\frac{3^{10}+1}{3^9+1}>1\Rightarrow A>\frac{3^{10}+1+2}{3^9+1+2}=\frac{3^{10}+3}{3^9+3}=\frac{3\left(3^9+1\right)}{3\left(3^8+1\right)}=\frac{3^9+1}{3^8+1}\)

Answer 4

\(\Rightarrow A>B\)

Answer 5

ai mà biết