Question : The third proportional to $\left(x^2-y^2\right)$ and $(x-y)$ is:
Option 1: $(x -y)$
Option 2: $\frac{x-y}{x+y}$
Option 3: $\frac{x+y}{x-y}$
Option 4: $(x + y)$
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Correct Answer: $\frac{x-y}{x+y}$
Solution :
We know,
The third proportional = $\frac{\text{(Second proportional)}^2}{\text{(First proportional)}}$
$= \frac{(x-y)^2}{x^2-y^2}$
$= \frac{(x-y)^2}{(x+y)(x-y)}$
$= \frac{(x-y)}{(x+y)}$
Hence, the correct answer is $\frac{(x–y)}{(x+y)}$.
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