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AP EAMCET201922 Apr 2019Morning ShiftMathematicsProperties of TrianglesActual

In ( A B C ), if (a, b ) and (c ) are in arithmetic progression, then ( A+2 B+ C= )

Options

  1. A1
  2. B2
  3. C( 3 2 )
  4. D( 3 +1 )

Correct answer

B. 2

Step-by-step solution

It is given, that in ( A B C, a, b, c ) are in ( AP ) So, (2 b=a+c )...(i) Now, ( A+2 B+2 C ) ( aligned = & b^2+c^2-a^2 2 b c +2 a^2+c^2-b^2 2 a c + a^2+b^2-c^2 2 a b = & a b^2+a c^2-a^3+2 a^2 b+2 c^2 b-2 b^3+a^2 c+b^2 c-c^3 2 a b c = & a b^2+a c^2-a^3+2 b (a^2+c^2 )-2 b^3+a^2 c+b^2 c-c^3 2 a b c = & -2 b^2+a c^2-a^3+(a+c) (a^2+c^2 ) 2 a b c = & -2 b^2 c-c^3+a^2 c+b^2 c-c^3 2 a b c = & a b^2+2 a c^2+2 c a^2+b^2 c-2 b^3 2 a b c = & b^2(a+c)+2 a c(a+c)-2 b^3 2 a b c = & b^2(2 b)+2 a c(2 b)-2 b^3 2 a b c =2 aligned )

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