Gọi a, b, c là b...

B

- Hướng dẫn giải

Đáp án B

$3^a=5^b=\frac{1}{3^c{5}^c}\iff \frac{a}{{\log }_{3}15}=\frac{b}{{\log }_{3}15}=-c{\log }_{15}15\iff \frac{a}{1+{\log }_{3}5}=\frac{b}{1+{\log }_{5}3}=-c$

Đặt $t={\log }_{3}5\Rightarrow \left\{\begin{array}{l}a=-c\left(1+t\right)\\ b=-c\left(1+\frac{1}{t}\right)=\frac{a}{t}\end{array}\Rightarrow a=-c\left(1+\frac{a}{b}\right)\iff ab+bc+ca=0\right.$

$\Rightarrow P={\left(a+b+c\right)}^2-4\left(a+b+c\right)\ge -4$. Dấu bằng khi $\left\{\begin{array}{l}a+b+c=2\\ ab+bc+ca=0\end{array}\right.$, chẳng hạn a = 2,b = c = 0.