restart;
g:=x->(x^2-5+alpha*x)/alpha;
#g:=x->(1/2)*(x+5/x);
alpha:=-3;
x0:=1.0;
x1:=g(x0);
x2:=g(x1);
x3:=g(x2);
x4:=g(x3);
x5:=g(x4);
x6:=g(x5);
A:=(t4,t5,t6)->t4-(t5-t4)^2/(t6-2*t5+t4);
x7:=A(x4,x5,x6);
sqrt(5.0);
x8:=g(x7);
x9:=g(x8);
A(x7,x8,x9);