已知x+y=1,xy=3/16,求x³y-2x²y²+xy³的值

已知x+y=1,xy=3/16,求x³y-2x²y²+xy³的值
已知x+y=1,xy=3/16,求x³y-2x²y²+xy³的值

已知x+y=1,xy=3/16,求x³y-2x²y²+xy³的值
x³y-2x²y²+xy³
=xy(x^2-2xy+y^2)
=xy(x^2+2xy+y^2-4xy)
=xy(x+y)^2-4(xy)^2
=3/16*1-4(3/16)^2
=3/64.

x³y-2x²y²+xy³=xy（x²-2xy+y²）=xy(x²+2xy+y²-4xy)=xy(x+y)²-4(xy)²=3/16×1-4(3/16)²=3/64.

由已知条件可求出x 和 y 然后代入 x=1/4 y=3/4 或x=3/4 y=1/4 这两种带入的结果是相同的

1. x+y=1,xy=3/16

2. (x+y)²=1,x²+y²+2xy=1,x²+y²-2xy=10/16,(x-y)²=10/16

3. x³y-2x²y²+xy³=xy(x-y)²=3/128