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Question
If r2 = pq , show that p : q is the duplicate ratio of (p+r) : ( q+r)
Solution
`"p"/"q" = ("p + q")^2/("q + r")^2`
`=> "p"/"q" = ("p"^2 + "r"^2 + 2"pr")/("q"^2 + "r"^2 + 2"qr")`
`=> "p"/"q" = ("p"^2 + "pq" + 2"pr")/("q"^2 + "pq" + 2"qr")`
⇒ pq2 +p2q+ 2pqr -p2q+pq2 + 2pqr
Since LHS = RHS, therefore p:q 1s the duplicate ratio of (p + r) : (q + r) .
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