已知集合M={x| |x-4| + |x-1|
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已知集合M={x| |x-4| + |x-1|
![已知集合M={x| |x-4| + |x-1|](/uploads/image/z/15403731-51-1.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88M%3D%7Bx%7C+%7Cx-4%7C+%2B+%7Cx-1%7C)
① x ≥ 4
x - 4 + x - 1 < 5
∴ M = [ 4 , 5 )
② x ≤ 1
4 - x + 1 - x < 5
∴ M = ( 0 , 1 ]
③ 1 < x < 4
4 - x + x - 1 < 5 恒成立
∴ M = ( 1 , 4 )
综上,得 M = ( 0 , 5 )
∵ N = ( a , 6 )
且 M ∩ N = ( 2 , b )
∴ M ∩ N = ( a , 5 )
∴ a = 2 , b = 5
∴ a + b = 7
x - 4 + x - 1 < 5
∴ M = [ 4 , 5 )
② x ≤ 1
4 - x + 1 - x < 5
∴ M = ( 0 , 1 ]
③ 1 < x < 4
4 - x + x - 1 < 5 恒成立
∴ M = ( 1 , 4 )
综上,得 M = ( 0 , 5 )
∵ N = ( a , 6 )
且 M ∩ N = ( 2 , b )
∴ M ∩ N = ( a , 5 )
∴ a = 2 , b = 5
∴ a + b = 7