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Question
If `(8a - 5b)/(8c - 5a) = (8a + 5b)/(8c + 5d)`, prove that `a/b = c/d`
Solution
`(8a - 5b)/(8c - 5a) = (8a + 5b)/(8c + 5d)`
⇒ `(8a + 5b)/(8a - 5b) = (8c + 5b)/(8c - 5d)` ...(using alternendo)
Applying componendo and dividendo,
`(8a + 5b + 8a - 5b)/(8a + 5b - 8a + 5b) = (8c + 5d + 8c - 5c)/(8c + 5d - 8c + 5d)`
∴ `(16a)/(10b) = (16c)/(10d)`
⇒ `a/b = c/d ...("Dividing by" 16/10)`
Hence proved.
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