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प्रश्न
If (7a + 8b)(7c – 8d) = (7a – 8b)(7c + 8d); prove that a : b = c : d.
उत्तर
Given, `(7a + 8b)/(7a - 8b) = (7c + 8d)/(7c - 8d)` ...(Invertendo)
Applying componendo and dividendo,
`(7a + 8b + 7a - 8b)/(7a + 8b - 7a + 8b) = (7c + 8d + 7c - 8d)/(7c + 8d - 7c + 8d)`
`=> (14a)/(16b) = (14c)/(16d)`
`=> a/b = c/d`
Hence, a : b = c : d.
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