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प्रश्न
If a : b = c : d, prove that: 5a + 7b : 5a – 7b = 5c + 7d : 5c – 7d.
बेरीज
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उत्तर
Given,
a : b = c : d
∴ `a/b = c/d`
Multiplying both sides by `5/7`
⇒ `(5a)/(7b) = (5c)/(7d)`
Applying componendo and dividendo:
⇒ `(5a + 7b)/(5a - 7b) = (5c + 7d)/(5c - 7d)`
Hence, it is proved that 5a + 7b : 5a − 7b = 5c + 7d : 5c − 7d.
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