Question
Find the fourth proportional to:
$2xy, x^2, y^2$
$2xy, x^2, y^2$
✓
Answer
Let A be the fourth proportional then
$2 x y: x^2=y^2: A $
$ \Rightarrow \frac{2 x y}{x^2}=\frac{y^2}{ A } $
$ \Rightarrow A =\frac{x^2 y^2}{2 x y} $
$ \Rightarrow A =\frac{x y}{2} .$
$2 x y: x^2=y^2: A $
$ \Rightarrow \frac{2 x y}{x^2}=\frac{y^2}{ A } $
$ \Rightarrow A =\frac{x^2 y^2}{2 x y} $
$ \Rightarrow A =\frac{x y}{2} .$
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