已知x-y=1/2,xy=8.求-1/2x³y-1/2xy³+x²y²的值.

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已知x-y=1/2,xy=8.求-1/2x³y-1/2xy³+x²y²的值.
已知x-y=1/2,xy=8.求-1/2x³y-1/2xy³+x²y²的值.

已知x-y=1/2,xy=8.求-1/2x³y-1/2xy³+x²y²的值.
-1/2x³y-1/2xy³+x²y²
=-1/2xy(x²+y²-2xy)
=-1/2xy(x-y)²
=-1/2×8×(1/2)²
=-1
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原式=-1/2xy(x²-2xy+y²)
=-1/2xy(x-y)²
=-1/2×8×(1/2)²
=-1

原式 = -1/2xy(x^2 -2xy + y^2)
= -1/2xy(x - y)^2
= -1/2 X 8 X (1/2)^2
= -1

收起

答案等于 -1