Question

what must be added to the terms of the ratio (p+q):(p-q) to make them equal to (p+q)^2:(p-q)^2​

Answer 1

Answer:

Let the term be equal to x

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

=> (p+q+x)/(p-q+x) = (p^2+q^2+2pq)/(p^2+q^2-2pq)

=> (p^2+q^2-2pq)(p+q+x) = (p^2+q^2+2pq)(p-q+x)

=> p^{3} + p^{2}q + p^{2}x + q^{2}p + q^{3} + q^{2}x - 2p^{2}q - 2pq^{2} - 2qpx = p^{3} - p^{2}q + p^{2}x + q^{2}p - q^{3} + q^{2}x + 2p^{2}q - 2pq^{2} + 2pqx

=> $\tt{2p^{2}q + 2q^{3} - 4p^{2}q = 4pqx}$

=> $\tt{x = \frac{(q^{2} - p^{2})}{2p}}$

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