Q. 5 A3.9( 8 Votes )

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

(a - c)2 = 4 (a - b) (b - c)

Answer :

(a - c)2 = 4 (a - b) (b - c)


a2 + c2 - 2ac = 4(ab – ac – b2 + bc)


a2 + 4c2b2 + 2ac - 4ab - 4bc = 0


(a + c - 2b)2 = 0


a + c - 2b = 0


Since a, b, c are in AP


b - a = c - b


a + c - 2b = 0


Hence,


(a - c)2 = 4 (a - b) (b - c)


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