# If (a – b), (b –

Given as (a – b), (b – c), (c – a) are in G.P (b – c)2 = (a – b)(c – a)

As we have to prove :(a + b + c)2 = 3(ab + bc + ca) so we proceed as follows:

b2 + c2 – 2bc = ac – a2 – bc + ab

a2 + b2 + c2 = ac + ab + bc

Add 2(ac + ab + bc) to both sides:

a2 + b2 + c2 + 2(ac + ab + bc) = ac + ab + bc + 2(ac + ab + bc)

(a + b + c)2 = 3(ab + bc + ca)

Hence Proved.

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