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If a, b, c are in A. P then prove that bc-aa, ca-bb, ab-cc also in A. P

If a, b, c are in A. P then prove that bc-aa, ca-bb, ab-cc also in A. P

Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
a+c = 2b
      Let bc-aa , ac-bb , ab-cc are in ap then we have to show that a, b , c are in Ap
Bc-aa + ab-cc = 2ac – 2b^2
  • (a+c)^2 – 2b^2 = ab + bc
  • Using a+c = 2b, (a+c)^2 = 4b^2
  • A+c = 2b => a,b,c are in AP 
    Cheers!!
    Regards,
    Vikas (B. Tech. 4th year
    Thapar University)

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