已知:| x + y + 1| +| xy - 3 | = 0,求代数式xy3 + x3y 的值.
问题描述：
已知:| x + y + 1| +| xy - 3 | = 0,求代数式xy3 + x3y 的值.
答
x+y+1=0------(x+y)^2=1------x^2+y^2+2xy=1
xy-3=0------xy=3
所以--------x^2+y^2=1-6=-5
xy^3+x^3y=xy(x^2+y^2)=3*(-5)=-15
答
绝对值相加为零.必然两者为零.解出XY 代入即可
答
∵| x + y + 1|≥0,| xy - 3 |≥0
| x + y + 1| +| xy - 3 | = 0,
∴x+y+1=0,即x+y=-1
xy=3
xy3 + x3y
=xy(x²+y²)
=yx[(x+y)²-2xy]
=3×(1-6)
=-15
答
| x + y + 1| +| xy - 3 | = 0,
x+y+1=0
xy-3=0
x+y=-1
xy=3
xy3 + x3y
=xy(y^2+x^2)
=xy[(x+y)^2-2xy)
=3[(-1)^2-2*3]
=2*(-5)
=-10