If 3 1 - aa + 9 = 19 - 3 a1 - a , then what is the value of a?

Answer: Option B

$$\begin{array}{rl}& \text{Put }\sqrt{\frac{1-a}{a}}=x\\ & \Rightarrow 3x+9=19-\frac{3}{x}\\ & \Rightarrow 3x+\frac{3}{x}=10\\ & \Rightarrow x=3,\frac{1}{3}\\ & \text{Now, }\sqrt{\frac{1-a}{a}}=3\\ & \Rightarrow \frac{1-a}{a}=9\\ & \Rightarrow 10a=1\\ & \Rightarrow a=\frac{1}{10}\\ & \text{and }\sqrt{\frac{1-a}{a}}=\frac{1}{3}\\ & \Rightarrow \frac{1-a}{a}=\frac{1}{9}\\ & \Rightarrow 10a=9\\ & \Rightarrow a=\frac{9}{10}\\ & \therefore a=\frac{1}{10}\text{and }\frac{9}{10}\end{array}$$