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Question
If r2 = pq, show that p : q is the duplicate ratio of (p + r) : (q + r).
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Solution
Given, r2 = pq
Duplicate ratio of (p + r) : (q + r)
= (p + r)2 : (q + r)2
= (p2 + r2 + 2pr) : (q2 + r2 + 2qr)
= (p2 + pq + 2pr) : (q2 + pq + 2qr)
= p(p + q + 2r) : q(q + p + 2r)
= p : q
Thus, p : q is the duplicate ratio of (p + r) : (q + r).
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