设集合A={(x,y)|y=—x²+2x+3,x∈R} B={(x,y)|y=5x²-10x+3,x∈R} 求A∩B设集合A={(x,y)|y=—x²+2x+3,x∈R}B={(x,y)|y=5x²-10x+3,x∈R}求A∩B
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![设集合A={(x,y)|y=—x²+2x+3,x∈R} B={(x,y)|y=5x²-10x+3,x∈R} 求A∩B设集合A={(x,y)|y=—x²+2x+3,x∈R}B={(x,y)|y=5x²-10x+3,x∈R}求A∩B](/uploads/image/z/13410521-17-1.jpg?t=%E8%AE%BE%E9%9B%86%E5%90%88A%3D%7B%28x%2Cy%29%7Cy%EF%BC%9D%E2%80%94x%26%23178%3B%2B2x%2B3%2Cx%E2%88%88R%7D+B%3D%7B%28x%2Cy%29%7Cy%3D5x%26%23178%3B-10x%EF%BC%8B3%2Cx%E2%88%88R%7D+%E6%B1%82A%E2%88%A9B%E8%AE%BE%E9%9B%86%E5%90%88A%3D%7B%28x%2Cy%29%7Cy%EF%BC%9D%E2%80%94x%26%23178%3B%2B2x%2B3%2Cx%E2%88%88R%7DB%3D%7B%28x%2Cy%29%7Cy%3D5x%26%23178%3B-10x%EF%BC%8B3%2Cx%E2%88%88R%7D%E6%B1%82A%E2%88%A9B)
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设集合A={(x,y)|y=—x²+2x+3,x∈R} B={(x,y)|y=5x²-10x+3,x∈R} 求A∩B设集合A={(x,y)|y=—x²+2x+3,x∈R}B={(x,y)|y=5x²-10x+3,x∈R}求A∩B
设集合A={(x,y)|y=—x²+2x+3,x∈R} B={(x,y)|y=5x²-10x+3,x∈R} 求A∩B
设集合A={(x,y)|y=—x²+2x+3,x∈R}
B={(x,y)|y=5x²-10x+3,x∈R}
求A∩B
设集合A={(x,y)|y=—x²+2x+3,x∈R} B={(x,y)|y=5x²-10x+3,x∈R} 求A∩B设集合A={(x,y)|y=—x²+2x+3,x∈R}B={(x,y)|y=5x²-10x+3,x∈R}求A∩B
元素是点
所以交集就是两个函数的交点
y=-x²+2x+3=5x²-10x+3
6x²-12x=0
6x(x-2)=0
x=0,x=2
y=-x²+2x+3=3,3
所以A∩B={(0,3),(2,3)}