Cho a, b là các số dương thỏa mãn

A

- Hướng dẫn giải

Đáp án A.

Ta có:

$$\begin{gathered} {\log }_{4}a={\log }_{25}b=\log \frac{4b-a}{2} \\ \iff \left\{\begin{array}{l}a=4^t;b={25}^t\\ 4b-a={2.10}^t\end{array}\right.. \end{gathered}$$

Khi đó

$$\begin{gathered} {4.25}^t-4^t={2.10}^t \\ \iff {\left(2^t\right)}^2+{2.2}^t{.5}^t-4.{\left(5^t\right)}^2=0 \\ \iff {\left[{\left(\frac{2}{5}\right)}^t\right]}^2+2.{\left(\frac{2}{5}\right)}^t-4=0 \end{gathered}$$

Vậy:

$$\begin{gathered} \frac{a}{b}=\frac{4^t}{{25}^t}={\left[{\left(\frac{2}{5}\right)}^t\right]}^2 \\ ={\left(-1+\sqrt{5}\right)}^2=6-2\sqrt{5}. \end{gathered}$$