Question

If a2 (b + c), b2(c + a), c2(a + b) are in A.P., show that either a, b, c are in A.P. or ab + bc +ca = 0.
what is A.P. here

Answer 1

A.P. arithmetic progression

Answer 2

thanks, what is G.P, geometric progression

Answer 3

can you help solve this

Answer 4

given condition implies that
b^2(c+a)-a^2(b+c)=c^2(a+b)-b^2(c+a)
Expanding and rearranging apprpriately

(b-a)(ab+bc+ca)=(c-b)(ab+bc+ca)
thus either ab+bc+ca = 0 or b-a=c-b which implies a.b.c are in AP