若a,b 为有理数,且5a^2-2ab+b^2+4a+1=0,求a^2b+ab^2的值

问题描述:

若a,b 为有理数,且5a^2-2ab+b^2+4a+1=0,求a^2b+ab^2的值

5a²-2ab+b²+4a+1=0
(2a+1)²+(a-b)²=0
2a+1=0 a=-1/2
a-b=0 b=a=-1/2
a²b+ab²=-1/8-1/8=-1/4