1、已知集合A={x|x²-4x+3=0},B={x|x²-ax+a-1=0},C={x|x²-mx+1=0},且A∪B=A,A∩C=C,求a,m的值或取值范围

1、
A = {x|x²-4x+3=0} = {1 ,3}
B = {x|x²-ax+a-1=0} = {1 ,a-1}
A∪B = A
a-1 = 3 ,a = 4
C = {x|x²-mx+1=0} ,A∩C=C
(1) C = Ф ,求a,m的值或取值范围
△ = m² - 4 < 0
-2 < m < 2
(2) C = {1}
△ = m² - 4 = 0 且 1 - m +1 = 0
m = 2
(3) C = {3}
△ = m² - 4 = 0 且 9 - 3m +1 = 0
无解
(4) C = {1 ,3}
1 - m +1 = 0 且 9 - 3m +1 = 0
无解
综上：-2 < m ≤ 2
2、
A = {x|2a≤ x ≤a+3} = [2a ,a+3]
B = {x|x＜-1或x＞5} = (-∞ ,-1) ∪ (5 ,+∞)
A∪B=R
2a ≤ -1 且 a + 3 ≥ 5
无解谢谢解答！第一题我算的也是a=4，但是答案上除了这个还有a=2，我有些不明白，解释一下，谢谢！是的：a = 2 ,a - 1 = 1B = {1}符合题目要求，我也漏解了！