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Question
If (4a + 9b)(4c – 9d) = (4a – 9b)(4c + 9d), prove that: a : b = c : d.
Solution
Given, `(4a + 9b)/(4a - 9b) = (4c + 9d)/(4c - 9d)`
Applying componendo and dividendo,
`(4a + 9b + 4a - 9b)/(4a + 9b - 4a + 9b) = (4c + 9d + 4c - 9d)/(4c + 9d - 4c + 9d)`
`(8a)/(18b) = (8c)/(18d)`
`a/b = c/d`
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