设全集I=R,已知集合M=﹛x|﹙x+3﹚²≤0﹜,N=﹛x|x²+x-6=0﹜
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设全集I=R,已知集合M=﹛x|﹙x+3﹚²≤0﹜,N=﹛x|x²+x-6=0﹜
﹙1﹚求﹙CIM﹚∩N﹔﹙2﹚记集合A=﹙CIM﹚∩N,已知集合B=﹛x|a-1≤x≤5-a,a∈R﹜,若B∪A=A,求实数a的取值范围
要详细步骤!
﹙1﹚求﹙CIM﹚∩N﹔﹙2﹚记集合A=﹙CIM﹚∩N,已知集合B=﹛x|a-1≤x≤5-a,a∈R﹜,若B∪A=A,求实数a的取值范围
要详细步骤!
![设全集I=R,已知集合M=﹛x|﹙x+3﹚²≤0﹜,N=﹛x|x²+x-6=0﹜](/uploads/image/z/1173696-24-6.jpg?t=%E8%AE%BE%E5%85%A8%E9%9B%86I%3DR%2C%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88M%3D%EF%B9%9Bx%7C%EF%B9%99x%EF%BC%8B3%EF%B9%9A%26%23178%3B%E2%89%A40%EF%B9%9C%2CN%3D%EF%B9%9Bx%7Cx%26%23178%3B%EF%BC%8Bx%EF%BC%8D6%3D0%EF%B9%9C)
(1)M = {x丨(x + 3)² ≤ 0}= {- 3}
N = {x 丨x ² + x - 6 = 0}= {- 3,2}
∴ CI M = {x 丨x ≠ - 3}
(CI M) ∩ N = {2}
(2)A = (CI M) ∩ N = {2}
∵ B ∪ A = A
∴① 当 B 为空集时,则:a - 1 > 5 - a
2 a > 6
a > 3
② 当 B 不为空集时,则:
a - 1 = 5 - a = 2
∴ a = 3
综上,a的取值范围是 a ≥ 3
N = {x 丨x ² + x - 6 = 0}= {- 3,2}
∴ CI M = {x 丨x ≠ - 3}
(CI M) ∩ N = {2}
(2)A = (CI M) ∩ N = {2}
∵ B ∪ A = A
∴① 当 B 为空集时,则:a - 1 > 5 - a
2 a > 6
a > 3
② 当 B 不为空集时,则:
a - 1 = 5 - a = 2
∴ a = 3
综上,a的取值范围是 a ≥ 3
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