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Find the Fourth Proportion to the Following: - ICSE Class 10 - Mathematics

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Question

Find the fourth proportion to the following: 

(p2q - qr2 ), (pqr - pr2 ) and (pq2 - pr2)

Solution

Let x be the fourth proportion 

`("p"^2"q" - "qr"^2) : ("pqr" - "pr"^2) :: ("pq"^2 - "pr"^2) :  x`


⇒ `("p"^2"q" - "qr"^2) xx "x" =  ("pqr" - "pr"^2) xx ("pq"^2 - "pr"^2)` 


⇒ x = `(("pqr" - "pr"^2) xx ("pq"^2 - "pr"^2))/(("p"^2"q" - "qr"^2))`


⇒ x = `("pr"("q" - "r") xx "p"("q"^2 - "r"^2))/("q"("p"^2 - "r"^2))`


⇒ x = `("pr"("q - r") xx "p"("q - r")("q + r"))/("q"("p"^2 - "r"^2))`


⇒ x = `("p"^2"r" ("q" - "r")^2 ("q" + "r"))/("q" ("p"^2 - "r"^2))`


The fourth proportion is `("p"^2"r" ("q" - "r")^2 ("q" + "r"))/("q" ("p"^2 - "r"^2))`

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APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.2 | Q: 2.3

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Solution Find the Fourth Proportion to the Following: Concept: Proportions.
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