Let a, b, c, d and p be any non zero distinct real numbers such that a2+b2+c2p2−2ab+bc+cdp+b2+c2+d2=0. ​Then:

a,b,c,d∈R° are all different  Given a2+b2+c2p2-2(ab+bc+cd)p+b2+c2+d2=0⇒(ap-b)2+(bp-c)2+(cp-d)2=0⇒ap-b=0 and bp-c=0 and cp-d=0⇒p=ba=cb=dc⇒a,b,c,d are in G.P