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MHT CET202613 April 2026Morning ShiftMathematicsProperties of TrianglesActual

With usual notations, in ABC , if 2a^2 = b^2 + c^2 , then 3A A + 2 =

Options

  1. Ab^2 - c^2 2bc
  2. B( b^2 - c^2 2bc )^2
  3. C( c^2 - b^2 bc )^2
  4. Dc^2 - b^2 bc

Correct answer

B. ( b^2 - c^2 2bc )^2

Step-by-step solution

Using the multiple angle formula, 3A = 4 ^3 A - 3 A . The given expression simplifies to: 3A A + 2 = 4 ^3 A - 3 A A + 2 = 4 ^2 A - 3 + 2 = 4 ^2 A - 1 By the cosine rule in ABC , we have: A = b^2 + c^2 - a^2 2bc Given that 2a^2 = b^2 + c^2 , we can substitute a^2 = b^2 + c^2 2 : A = b^2 + c^2 - b^2 + c^2 2 2bc = b^2 + c^2 4bc Substituting this into the simplified expression: 4 ^2 A - 1 = 4 ( b^2 + c^2 4bc )^2 - 1 = (b^2 + c^2)^2 4b^2 c^2 - 1 = (b^2 + c^2)^2 - 4b^2 c^2 4b^2 c^2 = b^4 + c^4 + 2b^2 c^2 - 4b^2 c^2 4b^2

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