Question

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

Answer 1

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