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Question
If a : b = c : d, show that (2a - 7b) (2c + 7d) = (2c - 7d) (2a + 7b).
Solution
We have
a: b = c : d
`a/b = c/d`
⇒ `(2a)/(7b) = (2c)/(7d) ...["Multiplying both side" 2/7]`
`["Using componendo and dividendo"]`
`(2a + 7b)/(2a - 7b) = (2c + 7d)/(2c - 7d)` ...[By cross multiplication]
⇒ (2a - 7b) (2c + 7d) = (2a + 7b) (2c - 7d).
Hence proved.
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