Question

已知集合A={(x,y)|y=x^2-6x+6,x∈R},B={(x,y)|y=-x^2+6x-6,x∈R},则A∩B=

Answer 1

令x²-6x+6=-x²+6x-6

x²-6x=-6

(x-3)²=3

x=3+√3,此时y=(3+√3)²-6(3+√3)+6=(3+√3-3)²-3=0

或

x=3-√3,此时y=(3-√3)²-6(3-√3)+6=(3-√3-3)²-3=0

A∩B={(3+√3,0),(3-√3,0)}