So sánh

- Hướng dẫn giải

Đáp án cần chọn là: D

$\begin{array}{l}A=\frac{2^5.7+2^5}{2^5{.5}^2-2^5.3}=\frac{2^5.(7+1)}{2^5.(5^2-3)}\\ =\frac{2^5.(7+1)}{2^5.(25-3)}=\frac{2^5.8}{2^5.22}=\frac{8}{22}=\frac{4}{11}\\ B=\frac{3^4.5-3^6}{3^4.13+3^4}=\frac{3^4.(5-3^2)}{3^4.(13+1)}\\ =\frac{3^4.(5-9)}{3^4.14}=\frac{3^4.(-4)}{3^4.14}\\ =\frac{-4}{14}=\frac{-2}{7}\end{array}$

MSC = 77

$\begin{array}{l}\frac{4}{11}=\frac{4.7}{11.7}=\frac{28}{77};\\ \frac{-2}{7}=\frac{-2.11}{7.11}=\frac{-22}{77}\end{array}$

Do đó $\frac{-22}{77}<\frac{28}{77}<1$ hay B < A < 1