1.

If a, b, c are in A.P., prove that : a2 + c2 + 4ac = 2 (ab + bc + ca)

Answer»

a2 + c2 + 4ac = 2 (ab + bc + ca) 

a2 + c2 + 2ac - 2ab - 2bc = 0 

(a + c - b)2 – b2 = 0 

a + c - b = b 

a + c - 2b = 0 

Since,

a, b, c are in AP 

b - a = c - b 

a + c - 2b = 0 

Hence proved.



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