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Question
If a : b : : c : d, then prove that
7a+11b : 7a -11b = 7c +11d : 7c - 11d
Solution
7a+11b: 7a -11b = 7c+11d : 7c -11d
`"a"/"b" = "c"/"d"`
Multiplying both sides by `7/11`
`=> "a"/"b" xx 7/11 = "c"/"d" xx 7/11`
`=> (7"a")/(11"b") = (7"c")/(11"d")`
Applying componendo and dividendo,
`(7"a" + 11"b")/(7"a" - 11"b") = (7"c" + 11"d")/(7"c" - 11"d")`
Hence, 7a+11b : 7a -11b = 7c +11d : 7c - 11d
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