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If (8a - 5b)/(8c - 5d) = (8a + 5b)/(8c + 5d), prove that a/b = c/d. - Mathematics

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Question

If `(8a - 5b)/(8c - 5d) = (8a + 5b)/(8c + 5d)`, prove that `a/b = c/d.`

Theorem
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Solution

`(8a - 5b)/(8c - 5d) = (8a + 5b)/(8c + 5d)`

Applying alternendo

⇒ `(8a - 5b)/(8a + 5d) = (8c - 5d)/(8c + 5d)`

Applying Componendo and Dividendo

⇒ `((8a - 5b) + (8a + 5d))/((8a - 5b) - (8a + 5d)) = ((8c - 5d) + (8c + 5d))/((8c - 5d) - (8c + 5d))`

⇒ `(16a)/(-10b) = (16c)/(-10d)`

⇒ `a/b = c/d`   ...(Dividing by `16/-10`)

Hence Proved.

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Chapter 7: Ratio and proportion - Exercise 7C [Page 138]

APPEARS IN

Nootan Mathematics [English] Class 10 ICSE
Chapter 7 Ratio and proportion
Exercise 7C | Q 5. | Page 138
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