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Question
If (7m +8n)(7p - 8q) = (7m - 8n)(7p + 8q), then prove that m: n = p: q
Solution
(7m +8n)(7p - 8q) = (7m - 8n)c
`=> (7"m" +8"n")/(7"m" - 8"n") = (7"p" + 8"q")/(7"p" - 8"q")`
Applying componendo and dividendo,
`(7"m" + 8"n" + 7"m" - 8"n")/(7"m" + 8"m" - 7"m" + 8"n") = (7"p" + 8"q" + 7"m" - 8"q")/(7"m" + 8"q" - 7"m" + 8"q")`
`=> (14 "m")/(16 "n") = (14"p")/(16"q")`
Dividing both sides by `14/16`
`"m"/"n" = "p"/"q"`
Hence. m:n = p : q .
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