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Question
If `(3x + 4y)/(3a + 4b) = (3x - 4y)/(3a - 4b),` prove that `x/y = a/b`.
Theorem
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Solution
We have given that:
⇒ `(3x + 4y)/(3a + 4b) = (3x - 4y)/(3a - 4b)`
⇒ (3x + 4y) (3a − 4b) = (3x − 4y) (3a + 4b)
Apply Componendo and Dividendo:
⇒ `((3x + 4y) + (3x - 4y))/((3x + 4y) - (3x - 4y)) = ((3a + 4b) + (3a - 4b))/((3a + 4b) - (3a - 4b))`
⇒ `(6x)/(8y) = (6a)/(8b)`
⇒ `(6x)/(8y) xx 8/6 = (6a)/(8b) xx 8/6`
⇒ `x/y = a/b`
Hence proved.
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