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Question
Find the third proportional to:
x - y, x2 - y2
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Solution
Let A be the third proportional then
(x - y) : (x2 - y2) = (x2 - y2) : A
⇒ `(x - y)/(x^2 - y^2) = (x^2 - y^2)/"A"`
⇒ A = `((x^2 - y^2))/(x - y)`
⇒ A = (x + y)(x2 - y2).
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