Question

If $x, y$ are real numbers such that $3^{(x / y)+1}-3^{(x / y)-1}=24$, then the value of $(x+y) /(x-y)$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (D)

We have,
$ 3^{(x / y)+1}-3^{(x / y)-1}=24 $
$\Rightarrow 3 \cdot 3^{x / y}-\frac{3^{x / y}}{3}=24$
$ \Rightarrow \frac{8}{3} \cdot 3^{x / y}=24 $
$\Rightarrow 3^{x / y}=9 $
$\Rightarrow 3^{x / y}=3^{2} $
$\Rightarrow \frac{x}{y}=2$
Using componendo and dividendo, we get
$\frac{x+y}{x-y}=\frac{2+1}{2-1} $
$\Rightarrow \frac{x+y}{x-y}=3$