Q10 of 176 Page 8

If a, b, c are in A.P., prove that:

(a + 2b — c)(2b + c — a)(c + a — b) = 4abc


[Hint: Put b = on L.H.S. and R.H.S.]

Given: a, b, c are in AP


∴ a + c = 2b …(i)


…(ii)


Now, taking LHS i.e. (a + 2b — c)(2b + c — a)(c + a — b)



[from (ii)]




⇒ 4abc


[from (ii)]


= RHS


Hence Proved


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