a+b=5,ab= -3,求a³b-2a²b²+ab³的值
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![a+b=5,ab= -3,求a³b-2a²b²+ab³的值](/uploads/image/z/1252938-66-8.jpg?t=a%2Bb%3D5%2Cab%3D+-3%2C%E6%B1%82a%26%23179%3Bb-2a%26%23178%3Bb%26%23178%3B%2Bab%26%23179%3B%E7%9A%84%E5%80%BC)
a+b=5,ab= -3,求a³b-2a²b²+ab³的值
a+b=5,ab= -3,求a³b-2a²b²+ab³的值
a+b=5,ab= -3,求a³b-2a²b²+ab³的值
a³b-2a²b²+ab³
=ab(a²-2ab+b²)
=ab(a-b)²
a+b=5,ab=-3
(a-b)²=(a+b)²-4ab=5²-4×(-3)=37
所以原式=ab(a-b)²
=-3×37
=-111
a³b-2a²b²+ab³
=ab(a²-2ab+b²)
=-3(a-b)²
=-3[(a+b)²-4ab]
=-3[25+12]
=-111
-111