Find the Fourth Proportional To: 2xy, X2, Y2

Find the fourth proportional to:
2xy, x², y²

Sum

Let A be the fourth proportional then
2xy : x² = y²: A
⇒ `(2xy)/x^2 = y^2/"A"`
⇒ A = `(x^2y^2)/(2xy)`
⇒ A = `(xy)/(2)`.

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