Question

1. What is the third proportion of (x2 - y2) and ( x - y)?
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Answer 1

Answer:

Hey mate,

here is your solution

Let the third proportional to (x² - y²) and (x - y) be P.

Therefore, (x² - y²), (x - y) and P are in proportion.

=> (x² - y²) : (x - y) = (x - y) : P

=> (x² - y²)/(x - y) = (x - y)/P

=> P = (x - y)²/(x² - y²)

=> P = (x - y)(x - y)/(x + y)(x - y)

=> P = (x - y)/(x + y).

Therefore, the third proportional to (x² - y²) and (x - y) is (x - y)/(x + y).