A={x||x-1|

A={x||x-1|

|x-1|

Given the set a = {x | X & # 178; - 2x-8 < 0} B = {x | X & # 178; - 3ax 2A & # 178; < 0}, if a ∪ B = a, find the value range of real number a

Solution a = {x | x ^ 2-2x-8 ＜ 0}
=｛x|(x-4)(x+2)＜0｝
=｛x/-2＜x＜4｝
B=｛x|x^2-3ax +2a^2＜0｝
=｛x|x^2-3ax +2a^2＜0｝
={x/(x-2a)(x-a)＜0}
From a ∪ B = a
Let B be a subset of A
know
When a = 0, B = {X / (x-0) (x-0) < 0} = an empty set, then B is a subset of A
When a > 0, B = {X / a < x < 2A},
Let B be a subset of A
Know 2A ≤ 4 and a ≥ - 2
That is - 2 ≤ a ≤ 2
That is, 0 < a ≤ 2
When a < 0, B = {X / 2A < x < a},
Let B be a subset of A
We know that a ≤ 4 and 2A ≥ - 2
That is - 1 ≤ a ≤ 4
That is - 1 ≤ a < 0
Therefore, it is known that - 1 ≤ a ≤ 2

The known set a = {x | x ^ 2-6x + 5

x^2-6x+5

X2-3ax + 2A2 = 0

x²－3ax＋2a²=0
(x－2a)(x－a)=0
1. If a ≠ 0, then X1 = 2A, X2 = a
2. If a = 0, then X1 = x2 = 0

Decomposition factor: x2 + 3ax-10a2-x + 2A

x2+3ax-10a2-x+2a
=（x+5a）（x-2a）-（x-2a）
=（x+5a-1）（x-2a）

Using the collocation method to solve the equation about X: x2 + 2A2 = 3ax

x²-3ax+9a²/4=a²/4
(x-3a/2)²=a²/2
x=3a/2+a/2 x=3a/2-a/2
X = 2A or x = a

Does B = {x | x2-3ax = 2A2} appear in the title and need to be discussed
Need to discuss?
When should we discuss that a is equal to 0 and a is not equal to 0?

x²－3ax－2a²=0
If it appears in the set as you show, it needs to be discussed. Reason: the elements in the set should be different from each other. If there are equal roots or unequal roots, it should be discussed in a non case. [in addition, if we study the relationship between set a and set B, we should also pay attention to the case that set a is an empty set]
If we only study the root of the equation, we must pay attention to the coefficient of quadratic term

Given the set a = {x L x ^ 2 + X-6 = 0}, B {x = l MX-1 = 0} if B is the proper subset of a, find the real number M

Hello! X & # 178; + X - 6 = 0 (X-2) (x + 3) = 0x = 2, x = - 3A = {2, - 3} MX - 1 = 0, when m = 0, - 1 = 0 does not hold, B = Φ, is the proper subset of A. when m ≠ 0, x = 1 / m only needs 1 / M = 2 or 1 / M = - 3, that is, M = 1 / 2 or M = - 1 / 3

Given the set = {- 1, a & # 178; - 3, a & # 178; - 3, a & # 178; + 1}, B = {A-3, A-1, a + 1}, and the intersection of a and B = {- 2}, find the value of real number a and the union of a and B

Is the element in set a repeated
Because a ∩ B = {- 2}, so - 2 ∈ a
Three elements in a, obviously - 1 ≠ - 2,
And a & # 178; + 1 must not be less than 1, so it is not - 2
Only a & # 178; - 3 = - 2
a²=1,a=±1
Because the element cannot be repeated, there is already element - 1 in a, so a = 1
Set a = {- 2, - 1,2}
B={-2,0,2}

Given the set a = {- 1, a & # 178; - 3, a & # 178; - 3, a & # 178; + 1}, and the intersection of a and B = {- 2}, find the value of real number a and the union of a and B

There can't be two A's in set A-3