geometric mean pls??

geometric mean of a set of real no:{a1,a2,a3.....,an} is Π(a1,a2,a3.....,an) ^(1/n)
so the geometric mean of a and c =(ac)^(1/2)=b--->b^2=ac
LHS=a(b+c)^2=a(b^2+2bc+c^2)=a(ac+2bc+c^2)=c(a^2+2ab+ac)=c(a^2+2ab+b^2)=RHS