A = {X / X * 2-3x + 2 = 0}, B = {X / AX-1 = 0} B is really contained in a, and the set of values of a is obtained

A = {X / X * 2-3x + 2 = 0}, B = {X / AX-1 = 0} B is really contained in a, and the set of values of a is obtained

A is x = 1, x = 2
If B is really contained in a, then B is an empty set or has only one element
If B is an empty set, then the equation AX-1 = 0 has no solution
So a = 0
If B has an element
Then B = {1} or {2}
x=1,a-1=0,a=1
x=2,2a-1=0,a=1/2
So a = 0, a = 1, a = 1 / 2

Find (1) (2) (3) for a given set a = {x ∈ R │ ax ^ 2-3x + 2 = 0}
The known set a = {x ∈ R │ ax ^ 2-3x + 2 = 0}
(1) If a = & Oslash;, find the value range of real number a;
(2) If a is a single element set, find the value of a and set a;
(3) Find the set P = {a ∈ R │ a such that a ≠ & Oslash;}
(1) a > 9/8
(2) When a = 0, a = {2 / 3}; when a = 9 / 8, a = {4 / 3}
(3) P = {a = R │ a such that a ≠ & Oslash;} = {a │ a ≤ 9 / 8}

(1) ∵A＝Ø
The equation AX ^ 2-3x + 2 = 0 has no real solution
∴△=3^2-4*a*2＜0
The results show that a > 9 / 8
(2) A is a set of single elements
① The equation AX ^ 2-3x + 2 = 0 is a quadratic equation of two variables about X
Then the equation has a unique real solution
That is △ = 3 ^ 2-4 * a * 20 = 0
The solution is a = 9 / 8, a = {4 / 3}
② The equation AX ^ 2-3x + 2 = 0 is a linear equation of one variable about X
Then the quadratic coefficient a = 0, a = {2 / 3}
(3) There are two types of discussion
① The equation AX ^ 2-3x + 2 = 0 is a quadratic equation of two variables about X
To make a ≠ & Oslash;
Then △ = 3 ^ 2-4 * a * 20 ≥ 0, a ≤ 9 / 8
② The equation AX ^ 2-3x + 2 = 0 is a linear equation of one variable about X
Then a = 0
In conclusion, P = {a = R │ a such that a ≠ & Oslash;} = {a │ a ≤ 9 / 8}

Let u = {x | X

A={2.3.5.7.9}
B={2.4.6.8}

Let u = {x ∈ Z | 0

(CUA) ∩ (cub) is the intersection of "the complement of a in U" and "the complement of B in U", only {3}. A ∪ B is the union of a and B, which is {1,2,4,5,6,7,8,9,10}. A ∩ B is the intersection of a and B, which is {4}

1.（x^2-3)^2+2(x^2-3)(x-3)+(x-3)^2
2.(x+1)(x+3)(x+5)(x+7)+15
3.x^2+y^2+4x+2y+3
4.(a^2+a+1)^2+2(a^2+a+1)(a^2+a-1)+(a^2+a-1)^2
5.(x^2+4)^2-16x^2
6.(a+b+c)^2-(a-b-c)^2
7.25(x-y)^2-16(x+y)^2
8.x^4-81x^2y^2
9.x^2(x-y)+y^2(y-x)
10.(a-b)(x-y)+(b-a)(x+y)
(multiplication)
11.2(2m-1)^2-3(m+1)(m-1)-2(m-1)^2
12.(2x+y+3t)(2x-y-3t)
13.(3a+1)^2(3a-1)^2
14.(2x-y)(2x+y)-(3x-y)(4x-y)
15.(-4x+2y)(-2y-4x)-(2x+3y)(8x-9y)
16.(2a+b-c)^2
- -

1.（x^2-3)^2+2(x^2-3)(x-3)+(x-3)^2
=(x^2-3+x-3)^2
=(x^2+x-6)^2
=(x+3)^2(x-2)^2
2.(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x)+22(x^2+8x)+105+15
=(x^2+8x)+22(x^2+8x)+120
=(x^2+8x+10)(x^2+8x+12)
=(x^2+8x+10)(x+2)(x+6)
3. X ^ 2 + y ^ 2 + 4x + 2Y + 3 - is the title wrong
x^2-y^2+4x+2y+3
=(x^2+4x+4)-(y^2-2y+1)
=(x+2)^2-(y-1)^2
=(x+2+y-1)(x+2-y+1)
=(x+y+1)(x-y+3)
4.(a^2+a+1)^2+2(a^2+a+1)(a^2+a-1)+(a^2+a-1)^2
=(a^2+a+1+a^2+a-1)^2
=(2a^2+2a)^2
=[2a(a+1)]^2
=4a^2(a+1)^2
5.(x^2+4)^2-16x^2
=(x^2+4+4x)(x^2+4-4x)
=(x+2)^2(x-2)^2
6.(a+b+c)^2-(a-b-c)^2
=(a+b+c+a-b-c)(a+b+c-a+b+c)
=2a(2b+2c)
=4a(b+c)
7.25(x-y)^2-16(x+y)^2
=[5(x-y)+4(x+y)][5(x-y)-4(x+y)]
=(9x-y)(x-9y)
8.x^4-81x^2y^2
=x^2(x^2-9y^2)
=x^2(x+3y)(x-3y)
9.x^2(x-y)+y^2(y-x)
=(x^2-y^2)(x-y)
=(x+y)(x-y)^2
10.(a-b)(x-y)+(b-a)(x+y)
=(b-a)(-x+y+x+y)
=2y(b-a)
(multiplication)
11.2(2m-1)^2-3(m+1)(m-1)-2(m-1)^2
=8m^2-8m+2-3m^2+3-2m^2+4m-2
=3m^2-4m+3
12.(2x+y+3t)(2x-y-3t)
=(2x)^2-(y+3t)^2
=4x^2-y^2-6ty-9t^2
13.(3a+1)^2(3a-1)^2
=[(3a+1)(3a-1)]^2
=(9a^2-1)^2
=81a^4-18a^2+1
14.(2x-y)(2x+y)-(3x-y)(4x-y)
=4x^2-y^2-(12x^2-7xy+y^2)
=-8x^2+7xy-2y^2
15.(-4x+2y)(-2y-4x)-(2x+3y)(8x-9y)
=(-4x)^2-(2y)^2-(16x^2+6xy-27y^2)
=16x^2-4y^2-16x^2-6xy+27y^2
=23y^2-6xy
16.(2a+b-c)^2
=(2a)^2+2·2a(b-c)+(b-c)^2
=4a^2+4ab-4ac+b^2-2bc+c^2
=4a^2+b^2+c^2+4ab-4ac-2bc

Factorization, urgent, online, etc
(1) 3x-710; 5-3x-8308; - 13X & sup3; - 11x & sup2; - 10x-6 (by group decomposition)
⑵(x+1)⁴+(x+3)⁴-272
⑶(ab-1)²+(a+b-2)（a+b-2ab）
⑷a²(b²-c²)-c²(b-c)(a+b)
⑸x³+6x²+11x+6
⑹x⁴+2x³+x²+1+2(x+x²)
⑺x⁴-2x²y-3y²+8y-4
⑻(y+z)9z+x0（x+y)+xyz
⑼xˆ5-3x⁴-x³+11x²-12x+4
⑽(x²+x-3)(x²+x-5)-3
⑾2x³-10x²+3x-15

The factorization of a ^ 2-2ab + B ^ 2-A + B-2

=(a-b）2-（a-b）-2
=[(a-b)-2]•[(a-b)+1]

kx^2+(2k-3)x+k-3
x^2+(n-2m)x+m^2-mn
kx^2+(3k+1)x+2k+1

kx^2+(2k-3)x+k-3
=(kx+k-3)(x+1)
x^2+(n-2m)x+m^2-mn
= x^2+(n-2m)x -m(n-m)
= (x-m)(x+n-m)
kx^2+(3k+1)x+2k+1
= (kx+2k+1)(k+1)
--------------------
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This is the result of X \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\#178; = [2 (x + y) - 5] ² = (2x + 2Y -...)

The great God of factorization comes in
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