[nutzz]

1---let ax^3+3bx^2+3 cx+d=0 and ax^2+2bx+c=0 have a common root then prove that (ac-b^2)(bd-c^2)>=0

2---given x,y are real numbers,x^2+y^2>0. if the maximum and minimum value of the expression E=x^2+y^2/x^2+xy+4y^2 are M and m, and A denotes the average value of M and m, compute A