Question

A={y|y=x²-4x+6，y∈N}，B={y|y=-x²-2x+18，y∈N}，求A∩B

Answer 1

A={y|y=x²-4x+6，y∈N}
={y| y =(x-2)^2+2,y∈N}
= { y| y= 2+n^2 , n∈0,1,2,3,..}
= { 2, 3, 6, 11, 18,.... }
B={y|y=-x²-2x+18，y∈N}
={y| y= -(x+1)^2+19, y∈N}
= { 19, 18, 15, 10, 3 }
A∩B = {3}

追问

={y| y =(x-2)^2+2,y∈N}
这个式子中的^这个是什么？

追答

]A={y|y=x²-4x+6，y∈N}
={y| y =(x-2)^2+2,y∈N}
= { 2, 3, 4,5,6,....}
B={y|y=-x²-2x+18，y∈N}
={y| y= -(x+1)^2+19, y∈N}
= { 1,2,3,...,19 }
A∩B = {2,3,4,5,....,19}

Answer 2

A与B相交，则x^2-4x+6 = -x^2-2x+18，解得x=3，x=-2
当X = 3时，y=3
当x = -2时，y=18
A∩B={y|3≤y≤18｝
7月o1

Answer 3

A∩B={2,3,4,5,6,7,8,...,19}

Answer 4

空集吧