Question

If ab + bc + ca
=/ 0 and a, b, c are in A.P., prove that a2(b + c), b2 (c + a), c2(a + b) are
also in A.P.​

Answer 1

Answer:

If x,y,z are in A.P. , xy=z−y

a2(b+c)−a2(b+c)=c2(a+b)−b2(c+a)

a2b+a2c−a2b−a2c=c2a+c2b−b2c−b2a

(a2b−a2c)+(b2a−a2b)=(c2a−b2a)+(c2b−b2c)

c(b2−a2)+ab(b−a)=a(c2−b2)+bc(c−b)

(b−a)[c(b+a)+ab]=(c−b)[a(c+b)+bc]

(b