Question

so sanh

\(A=\frac{3^{123}+1}{3^{125}+1}\)va \(b=\frac{3^{122}+1}{3^{134}+1}\)

Answer 1

Đề đúng là \(B=\frac{3^{122}+1}{3^{124}+1}\)nhé .

Ta có :

\(9A=9.\left(\frac{3^{123}+1}{3^{125}+1}\right)=\frac{3^{125}+9}{3^{125}+1}\)

\(=1+\frac{8}{3^{125}+1}\)

\(9B=9.\left(\frac{3^{122}+1}{3^{124}+1}\right)=\frac{3^{124}+9}{3^{124}+1}\)

\(=1+\frac{8}{3^{124}+1}\)

Dễ thấy \(3^{124}+1< 3^{125}+1\)

\(\Leftrightarrow\frac{8}{3^{125}+1}< \frac{8}{3^{124}+1}\)

\(\Leftrightarrow\frac{8}{3^{125}+1}+1< \frac{8}{3^{124}+1}+1\)

\(\Leftrightarrow A< B\)

Vậy....