Question

if (a-b),(b-c),(c-a) are in gp then value of (a+b+c)^2 - 3(ab+bc+CA)​

Answer 1

The relation between the a,b,c is that the a2+b2+c2=ab+bc+ca.

a-b,b-c,c-a

t1 t2 t3

If a,b,c are in G.P then we use the formula t2/t1=t3/t2

b-c/a-b=c-a/b-c

(b-c)(b-c)=(a-b)(c-a)

By solving this we get the answer. That is a2+b2+c2=ab+bc+ca.