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
$\frac{x+y}{x-y}=\frac{2+1}{2-1}$
$\Rightarrow \frac{x+y}{x-y}=3$