化简求值：已知x+y=2,xy=0.75,求x的3次方y+xy的3次方+2x的2次方y的3次方

x^3y+xy^3+2x^2y^3
=xy(x^2+y^2+2xy^2)
=xy[(x+y)^2+2xy^2-2xy]
=xy[(x+y)^2+2xy(y-1)]
=(3/4)[4+3(y-1)/2]
=3+9(y-1)/8
=15/8+9y/8
x+y=2 xy=3/4
x,y是方程4x^2-8x+3=0的两根
(2x-1)(2x-3)=0
x1=1/2 x2=3/2
即y的取值为1/2或3/2,分别代入
15/8+9*(1/2)/8=39/16
15/8+9*(3/2)/8=57/16