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Question
Find the third proportional to:
`a/b + b/c, sqrt(a^2 + b^2)`.
Solution
Let x be the third proportional then
`a/b + b/c, sqrt(a^2 + b^2) = sqrt(a^2 + b^2) : x`
⇒ `(a^2 + b^2)/(ab) : sqrt(a^2 + b^2) = sqrt(a^2 + b^2) : x`
⇒ `(a^2 + b^2)/(ab sqrt(a^2 + b^2)) = sqrt(a^2 + b^2)/x`
⇒ x = `(ab (a^2 + b^2))/((a^2 + b^2))`
⇒ x = ab.
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