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AP EAMCET202316 May 2023Evening ShiftMathematicsSequences and SeriesActual

In ABC , if a, b, c are in arithmetic progression and C =2 ~A , then a : c =

Options

  1. A4: 5
  2. B2: 3
  3. C5: 6
  4. D3 : 2

Correct answer

B. 2: 3

Step-by-step solution

Given that a, b, c are in A.P aligned & b = a + c 2 (i) & And C =2 ~A C = 2 ~A =2 A A & C =2 a ( b ^2+ c ^2- a ^2 ) 2 bc & 2 c ^3+3 a ^3-3 ac ^2-2 a ^2 c =0 & 3 ( a c )^3-2 ( a c )^2-3 ( a c )+2=0 & (3 ( a c )-2 ) [ ( a c )^2-1 ]=0 a c = 2 3 =2: 3 aligned

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