Let K = Q(x) be the field of rational functions in one variable x over Q. Let K1 K be the field K1 = Q(x^2 ) (of rational functions in x^2 ) and let K2 = Q(x^2 x). (a) Show that K is algebraic over K1 and K2 (write explicitly the minimal polynomial of x K over these fields). (b) Show that K is not algebraic over K1 K2 (compute K1 K2).