If a, b, c are in G.P., prove that :
a(b2 + c2) = c(a2 + b2)
Now, as a,b,c are in GP.
Using the idea of geometric mean we can write –
∴ b2 = ac …(1)
Put in the LHS of the given equation to be proved –
LHS = a(ac + c2) {putting b2 = ac}
⇒ LHS = a2c + ac2
⇒ LHS = c(a2 + ac)
Again put ac = b2
⇒ LHS = c(a2 + b2) = RHS
∴ L.H.S = R.H.S
Hence proved