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If a, b, c are in AP, show that(a + 2b – c)(2b + c – a)(c + a – b) = 4abc. |
Answer» To prove: (a + 2b – c)(2b + c – a)(c + a – b) = 4abc. Given: a, b, c are in A.P. Proof: Since a, b, c are in A.P. ⇒ 2b = a + c … (i) Taking LHS = (a + 2b – c) (2b + c – a) (c + a – b) Substituting the value of 2b from eqn. (i) = (a + a + c – c) (a + c + c – a) (c + a – b) = (2a) (2c) (c + a – b) Substituting the value of (a + c) from eqn. (i) = (2a) (2c) (2b – b) = (2a) (2c) (b) = 4abc = RHS Hence Proved |
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