Question

已知x≠y，且使等式x²+x-3=0，y²+y-3=0，则x²y+xy²=

Answer 1

x²y+xy²= -3

令 x²+x-3=0....................................1
y²+y-3=0......................................2
方程1-2得
x²-y²+x-y=0
即（x-y)(x+y+1）=0
x≠y则x+y+1=0
x+y=-1
方程1+2得
x²+y²+x+y-6=0
因为x+y=-1
则x²+y²=7
(x+y)²=x²+y²+2xy=7+2xy=1
则xy=-3
x²y+xy²= xy(x+y)=-3

Answer 2

因为x≠y，所以x,y是方程a^2+a-3=0的两个不同实数根
所以x+y=-1,xy=-3
x²y+xy²= xy(x+y)=3

Answer 3

=5