Verified answer

x²+3x-28=0

x1+x2= -3

x1*x2= -28

1/x1 + 1/x2= (x2+x1)/x1*x2= 3/28

x1²x2+x1x2²= x1x2(x1+x2)= 84

x1²+x2²= (x1+x2)²-2x1x2= (-3)²-2*(-28)= 9+56=65