设集合A=﹛﹙x,y﹚|ay²-x-1=0﹜,B=﹛﹙x,y﹚|4x²+2x-2y+5=0﹜,C=﹛﹙x,y﹚|y=kx+b﹜⑴若a=0,求A∩B⑵若a=1,且存在自然数k和b,使得﹙A∩C﹚∪﹙B∩C﹚=空集,求k和b的值
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![设集合A=﹛﹙x,y﹚|ay²-x-1=0﹜,B=﹛﹙x,y﹚|4x²+2x-2y+5=0﹜,C=﹛﹙x,y﹚|y=kx+b﹜⑴若a=0,求A∩B⑵若a=1,且存在自然数k和b,使得﹙A∩C﹚∪﹙B∩C﹚=空集,求k和b的值](/uploads/image/z/2724253-61-3.jpg?t=%E8%AE%BE%E9%9B%86%E5%90%88A%3D%EF%B9%9B%EF%B9%99x%2Cy%EF%B9%9A%7Cay%26%23178%3B%EF%BC%8Dx%EF%BC%8D1%3D0%EF%B9%9C%2CB%3D%EF%B9%9B%EF%B9%99x%2Cy%EF%B9%9A%7C4x%26%23178%3B%EF%BC%8B2x%EF%BC%8D2y%EF%BC%8B5%3D0%EF%B9%9C%2CC%3D%EF%B9%9B%EF%B9%99x%2Cy%EF%B9%9A%7Cy%3Dkx%EF%BC%8Bb%EF%B9%9C%E2%91%B4%E8%8B%A5a%3D0%2C%E6%B1%82A%E2%88%A9B%E2%91%B5%E8%8B%A5a%3D1%2C%E4%B8%94%E5%AD%98%E5%9C%A8%E8%87%AA%E7%84%B6%E6%95%B0k%E5%92%8Cb%2C%E4%BD%BF%E5%BE%97%EF%B9%99A%E2%88%A9C%EF%B9%9A%E2%88%AA%EF%B9%99B%E2%88%A9C%EF%B9%9A%3D%E7%A9%BA%E9%9B%86%2C%E6%B1%82k%E5%92%8Cb%E7%9A%84%E5%80%BC)
设集合A=﹛﹙x,y﹚|ay²-x-1=0﹜,B=﹛﹙x,y﹚|4x²+2x-2y+5=0﹜,C=﹛﹙x,y﹚|y=kx+b﹜⑴若a=0,求A∩B⑵若a=1,且存在自然数k和b,使得﹙A∩C﹚∪﹙B∩C﹚=空集,求k和b的值
设集合A=﹛﹙x,y﹚|ay²-x-1=0﹜,B=﹛﹙x,y﹚|4x²+2x-2y+5=0﹜,C=﹛﹙x,y﹚|y=kx+b﹜
⑴若a=0,求A∩B
⑵若a=1,且存在自然数k和b,使得﹙A∩C﹚∪﹙B∩C﹚=空集,求k和b的值
设集合A=﹛﹙x,y﹚|ay²-x-1=0﹜,B=﹛﹙x,y﹚|4x²+2x-2y+5=0﹜,C=﹛﹙x,y﹚|y=kx+b﹜⑴若a=0,求A∩B⑵若a=1,且存在自然数k和b,使得﹙A∩C﹚∪﹙B∩C﹚=空集,求k和b的值
(1)a=0,x=-1
代入B得:y=3.5
A∩B=(-1,3.5)
(2)即A∩C=0,B∩C=0
(kx+b)^2-x-1=0,4x^2+2x-2(kx+b)+5=0无解
即(2kb-1)^2-4k^2(b^2-1)
1,A∩B=(-1,3.5)
2,k=1,b=2