神马作文网已知x+y=4,xy=3,求：（1）x^2y-xy^2;（2）(x^2+1)(y^2+1)
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已知x+y=4,xy=3,求：（1）x^2y-xy^2;（2）(x^2+1)(y^2+1)
x+y=4,xy=3
(x-y)^2=(x+y)^2-4xy
(x-y)^2=4^2-4*3
(x-y)^2=16-12
(x-y)^2=4
x-y=±2
x^2y-xy^2
=xy(x-y)
=±2*3
=±6
(x^2+1)(y^2+1)
=x^2(y^2+1)+(y^2+1)
=x^2y^2+x^2+y^2+1
=x^2y^2+x^2+y^2+2xy-2xy+1
=x^2y^2-2xy+1+x^2+y^2+2xy
=(xy-1)^2+(x+y)^2
=(3-1)^2+4^2
=2^2+16
=4+16
=20
(x-y)^2=(x+y)^2-4xy
(x-y)^2=4^2-4*3
(x-y)^2=16-12
(x-y)^2=4
x-y=±2
x^2y-xy^2
=xy(x-y)
=±2*3
=±6
(x^2+1)(y^2+1)
=x^2(y^2+1)+(y^2+1)
=x^2y^2+x^2+y^2+1
=x^2y^2+x^2+y^2+2xy-2xy+1
=x^2y^2-2xy+1+x^2+y^2+2xy
=(xy-1)^2+(x+y)^2
=(3-1)^2+4^2
=2^2+16
=4+16
=20
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