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# What Quantity Must Be Added to Each Term of the Ratio (P + Q) : (P - Q) to Make It Equal to (P + Q)2 : (P - Q)2 ? - ICSE Class 10 - Mathematics

#### Question

What quantity must be added to each term of the ratio (p + q) : (p - q) to make it equal to (p + q)2 : (p - q)2 ?

#### Solution

Let x be added from each term such that

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

⇒ (p + q + x)(p2 - 2pq+ q2 ) = (p2 + 2pq + q2)(p- q + x)

⇒ p3 + p2 q + p2x + q2p + q3 + q2x - 2p2q - 2pq2 - 2pqx

⇒ p3 - p2q + p2 x + q2p - q3 + q2x + 2p2q - 2pq2 + 2pqx

⇒ p2q + q3 - 2 p2q- 2pqx = -p2q - q3 + 2p2 q + 2pqx

⇒ 2q3 - p2q = 4pqx

⇒ 2q( q2 - p2 ) = 4pqx

⇒  x = ("q"^2 - "p"^2)/(2"p")

("q"^2 - "p"^2)/(2"p") should be added to each term.

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#### APPEARS IN

Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.1 | Q: 20

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Solution What Quantity Must Be Added to Each Term of the Ratio (P + Q) : (P - Q) to Make It Equal to (P + Q)2 : (P - Q)2 ? Concept: Ratio and Proportion Example.
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