Cho x, y là các số thực dương thỏa mãn

D

- Hướng dẫn giải

Đáp án D

Đặt ${\log }_{25}\frac{x}{2}={\log }_{15}y={\log }_9\frac{x+y}{4}=t\Rightarrow \left\{\begin{array}{l}\frac{x}{2}={25}^t\\ y={15}^t\\ x+y=4.9^t\end{array}\right.$ 

$\Rightarrow \left\{\begin{array}{l}2.{15}^t+{15}^t=4.9^t\\ \frac{x}{y}=2{\left(\frac{5}{3}\right)}^t\end{array}\right.\Rightarrow 2.{\left(\frac{5}{3}\right)}^{2t}+{\left(\frac{5}{3}\right)}^t-4=0\iff [\begin{array}{l}{\left(\frac{5}{3}\right)}^t=\frac{-1+\sqrt{33}}{4}\\ {\left(\frac{5}{3}\right)}^t=\frac{-1-\sqrt{33}}{4}\end{array}$

$\Rightarrow {\left(\frac{5}{3}\right)}^t=\frac{-1+\sqrt{33}}{4}\Rightarrow \frac{x}{y}=\frac{-1+\sqrt{33}}{4}\Rightarrow \left\{\begin{array}{l}a=-1\\ b=33\end{array}\Rightarrow a+b=32\right.$.