已知x+y=1,xy=3/16,求x³y-2x²y²+xy³的值
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![已知x+y=1,xy=3/16,求x³y-2x²y²+xy³的值](/uploads/image/z/976118-14-8.jpg?t=%E5%B7%B2%E7%9F%A5x%2By%3D1%2Cxy%3D3%2F16%2C%E6%B1%82x%26%23179%3By-2x%26%23178%3By%26%23178%3B%2Bxy%26%23179%3B%E7%9A%84%E5%80%BC)
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
x+y=1,xy=3/16 (x+y)²=1,x²+y²+2xy=1,x²+y²-2xy=10/16,(x-y)²=10/16 x³y-2x²y²+xy³=xy(x-y)²=3/128