Question

(X-Y)², (X²-Y²)², find the third proportional
the answer should be (X+Y)⁴(X-Y)²​

Answer 1

Answer:

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).

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