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Question
If a : b : : c : d, prove that (2a + 3b)(2c – 3d) = (2a – 3b)(2c + 3d)
Solution
∵ a : b :: c : d
∴ `a/b = c/d`
⇒ `(2a)/(3b) = (2c)/(3d) ...("Multiply by" 2/3)`
Applying componendo and dividendo,
`(2a + 3b)/(2a - 3b) = (2c + 3d)/(2c - 3d)`
⇒ (2a + 3b)(2c – 3d)
= (2a – 3b)(2c + 3d) ...(By corss multiplication).
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