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

问题描述:

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/8x+y=2 xy=3/4x,y是方程4x^2-8x+3=0的两根(2x-1)(2x-3)=0x1=1/2 x2=3/2即y的取值为1/2或3/...