Set a = {x | X & sup2; - 3x + 2 = 0}, B = {x | X & sup2; + 2 (a + 1) x + A & sup2; - 5 = 0} (1) If a ∩ B = {2}, find the value of A (2) If a ∪ B = a, find the value range of A (3) If u = R, a ∩ (cub) = a, find the value range of real number a

Set a = {x | X & sup2; - 3x + 2 = 0}, B = {x | X & sup2; + 2 (a + 1) x + A & sup2; - 5 = 0} (1) If a ∩ B = {2}, find the value of A (2) If a ∪ B = a, find the value range of A (3) If u = R, a ∩ (cub) = a, find the value range of real number a

A: (X-2) (x-1) = 0, so a = {1,2}
(1) Because a ∩ B = {2}, x = 2 is a solution of B, substituting 4 + 4 (a + 1) + A2-5 = 0
Therefore, a 2 + 4A + 3 = 0 gives a = - 1 or a = - 3, both of which are consistent
(2) Because a ∪ B = a, when B is an empty set, △ 0, the solution is a < - 3
If B is not an empty set, a ≥ - 3, if a ∪ B = a, then B can only be {1} or {2} or {1,2} because {1} or {2} means that B has only one root, so when B is {1} or {2}, △ should be = 0, that is, a = - 3, when a = - 3, the solution is x = 2, so a = - 3 meets the condition
When B = {1,2}, how to use the Vader formula to know whether there is such a
In conclusion: a ≤ - 3
（3）
If a ∩ (cub) = a, then a ∩ B must be an empty set
If B is an empty set, then a ＜ - 3 satisfies the condition
From (2), we know that the set of B cannot have the solution {1,2}. When the solution of B contains 1, we get a = √ 3-1, or a = - √ 3-1
When the solution of B contains the solution of 2, we get x = - 1 or x = - 3
So the value range of a is that a cannot be equal to - √ 3-1, a = √ 3-1, x = - 1, x = - 3

The known set a = {xl-2}

The minimum value in the set a is greater than or equal to a is a greater than or equal to - 2

Given that x is a real number, y is a pure imaginary number, and satisfies (2x-1) + (3-y) I = Y-I, find x, y

Because y is a pure imaginary number, let y = Bi, (B ∈ R, and B ≠ 0). The original formula can be sorted as (2x-1) + (3-bi) I = bi-i, that is, (2x-1 + b) + 3I = (B-1) I. from the definition of complex number equality, we can get: 2x − 1 + B = 0b − 1 = 3, the solution is b = 4x = − 32, so x = − 32, y = 4I

How to express the set of solutions of equations by description

For example, the solution of X & # 178; - 5x + 6 = 0 can be expressed as
{x | X & # 178; - 5x + 6 = 0} is so simple, just copy in the equation
If y & # 178; - 5Y + 6 = 0
Note that the unknowns before and after {x | X & # 178; - 5x + 6 = 0} or {y | Y & # 178; - 5Y + 6 = 0} should be consistent, and other equations of a, B, C can also be used
If X & # 178; - 5Y + 6 = 0, then
Because there are two unknowns
We should pay attention to the above special cases
More questions can help me~