If (3a + 6b + c + 2d) × (3a - 6b - c + 2d) = (3a - 6b + c - 2d) × (3a + 6b - c - 2d), then which one of the following is correct?

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CDS Elementary Mathematics 3 Sep 2023 Official Paper
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  1. ab = cd
  2. ac = bd
  3. ad = bc
  4. ad + bc = 0

Answer (Detailed Solution Below)

Option 3 : ad = bc
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Detailed Solution

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Concept Used:

If \(\frac{a+b}{a-b}\) = \(\frac{c+d}{c-d}\) then \(\frac{a}{b}\) = \(\frac{c}{d}\)

Calculation:

(3a + 6b + c + 2d) × (3a - 6b - c + 2d) = (3a - 6b + c - 2d) × (3a + 6b - c - 2d)

⇒ (3a + 6b + c + 2d)/(3a - 6b + c - 2d) = (3a + 6b - c - 2d)/(3a - 6b - c + 2d)

⇒ (3a + c) + (6b + 2d)/(3a + c) - (6b + 2d) = (3a - c) + (6b - 2d)/(3a - c) - (6b - 2d)

⇒ (3a + c)/(6b + 2d) = (3a - c)/(6b - 2d)

⇒ (3a + c)/(3a - c) = (6b + 2d)/(6b - 2d)

 3a/c = 6b/2d

 a/c = b/d

 ad = bc

∴ The correct option is 3 which is ad = bc.

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