Question

已知x+y=4,xy=3,求：（1）x^2y-xy^2;（2）(x^2+1)(y^2+1)求解

Answer 1

x²y-xy²
=xy(x-y)
=3×4
=12

(x²+1)(y²+1)
=x²y²+x²+y²+1
=(x²y²+2xy+1)+(x²-2xy+y²)
=(xy+1)²+(x-y)²
=(3+1)²+4²
=16+16
=32

很高兴为您解答，祝你学习进步！【the 1990】团队为您答题。
有不明白的可以追问！如果您认可我的回答。
请点击下面的【选为满意回答】按钮。
如果有其他问题请另发或点击向我求助，答题不易，请谅解，谢谢！

Answer 2

x+y=4,xy=3，所以(x-y)²=(x+y)²-4xy=16-4*3=4，所以x-y=±2
1、x^2y-xy^2=xy(x-y)=6(x>y时)或-6(x<y时)
2、(x^2+1)(y^2+1)=(xy)^2+(x^2+y^2)+1=9+1+(x+y)^2-2xy=10+16-6=20

Answer 3

x+y=4,xy=3，所以(x-y)²=(x+y)²-4xy=16-4*3=4，所以x-y=±2
1）x^2*y-x*y^2=xy(x-y)=±6;
2)(x^2+1)(y^2+1)=(xy)^2+x^2+y^2+1=(xy)^2+(x+y)^2-2xy+1=3^2+4^2-2*3+1=20

Answer 4

(x-y)^2=(x+y)^2-4xy=16-12=4
x-y=+-2
1）x^2y-xy^2
=xy(x-y)=+-6
（2）(x^2+1)(y^2+1)
=x^2t^2+x^2+y^2+1
=x^2y^2+(x+y)^2-2xy+1
=9+16-6+1
=20

Answer 5

x+y=4
xy=3
(1) (x-y)²=(x+y)²-4xy
=16-4*3
=4
x-y=±2
x²y-xy²=xy(x-y)
=±6
即 x²y-xy²=6 或 x²y-xy²=-6
(2) (x²+1)(y²+1)
=(xy)²+x²+y²+1
=(xy)²+(x+y)²-2xy+1
=9+16-2*3+1
=20