Question

The third proportional to $(x^2 - y^2)$ and (x - y) is:

• A. (x - y)
• B. $$\frac{(x-y)}{(x+y)}$$
• C. $$\frac{(x+y)}{(x-y)}$$
• D. (x + y)

Answer 1

Answer:

$$\frac{(x-y)}{(x+y)}$$

Given:

First number (a) $=x^2-y^2$

Second number (b) = (x - y)

Formula used:

Third proportional $=\frac{(2nd number(a))^2}{first number(b)}$

$(x^2-y^2)=(x-y)\times{(x+y)}$

Calculation:

Third proportional $=(x-y)^2\times{(x^2-y^2)}$

$⇒\frac{(x-y)\times(x-y)}{(x-y)\times(x+y)}$

$⇒\frac{(x-y)}{(x+y)}$

∴ The correct answer is $\frac{(x-y)}{(x+y)}$