If a, b, c are in G.P, then
ba=cb⇒=b2a2=c2b2 ⇒b2+a2a2=c2+b2b2 ⇒b2+a2a2=c2+b2ac ∴ c(b2+a2)=a(c2+b2)
Write the following by using ∑ notation
(1) ab(a + b) + bc(b + c) + ca(c + a)
(2) a2 + b2 + c2 − ab − bc − ca
(3) x(y2 + z2) + y(z2 − x2) + z(x2 − y2)
(4) ab2 − ac2 − a2b + bc2 − cb2 + ca2