1.

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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