Given a = empty set, B = {Xi (x + 1). (X & sup2; + 3x-4) = 0, X ∈ r} A is really contained in C and contained in B. find the set C satisfying the condition

Given a = empty set, B = {Xi (x + 1). (X & sup2; + 3x-4) = 0, X ∈ r} A is really contained in C and contained in B. find the set C satisfying the condition

A=ø is subset of any set
A is really contained in C = > C is a non empty set
B={x|(x+1).(x²+3x-4）=0 x∈R}
= {x|(x+1)(x+4)(x-1)=0 x∈R}
= {-4,-1,1}
C is contained in B = > C is a subset of {- 4, - 1,1}
A is really contained in C is contained in B = > C is a non empty subset of {- 4, - 1,1}
{-4},{-1},{1}, {-4,-1},{-4,1},{-1,1}, {-4,-1,1}
The known set a = {x | x-3 / X-1 ≤ 0}, B = {x | 2-3x-c ≤ 0}
1: If a is contained in B, find C;
2: If B is contained in a, find C
1) : x-3 / X-1 ≤ 0.2-3x-c ≤ 0.2): (the process of solving inequality is the same as before)
1≤x≤3 ,x≠1 x≥c-2／-3 ∵B∈A
Ψ 1 ＜ x ≤ 3 ℅ C-2 / - 3 ≥ 1 and C-2 / - 3 ≤ 3
∵A∈B ∴-7≤c≤-1
‖ C-2 / - 3 ≤ 1 or C-2 / - 3 ≥ 3
 C ≥ - 1 or C ≤ - 7
Given the set a = {x ∈ R | ax2-3x + 2 = 0, a ∈ r}, if there is at most one element in a, then the value range of a is______ .
From the meaning of the question, there is at most one solution to the equation ax2-3x + 2 = 0, a ∈ R. ① when a = 0, there is only one solution to the equation - 3x + 2 = 0; ② when a ≠ 0, there is at most one solution to the equation ax2-3x + 2 = 0, a ∈ R, then △ = 9-8a ≤ 0, a ≥ 98. In conclusion, the value range of a is a = 0 or a ≥ 98, so the answer is: a = 0 or a ≥ 98
Given the square of a = 3B - the square of 2a, B = the square of ab-2b - the square of a, find the value of a-2b, where a = 2, B = minus 1 / 2
Given X-Y = 2, then the value of the algebraic formula - 2x + 2Y is:
If a and B are reciprocal and X and y are opposite, then (x + y) B is divided into a-ab=
1、
-2x+2y
=-2（x-y）
=-2×2
=-4
2、
From the meaning of the title:
ab=1
x+y=0
So:
simple form
=0×1-1
=-1
Urgent need for factoring 100 questions (including answers)
Go to the website of senior high school entrance examination
What is the square of (a-2b) + (a-b) (a + b) - 2 (a-3b) (a-b) when a = 1 / 2 and B = - 3?
(a-2b)²+(a-b)(a+b)-2(a-3b)(a-b)=(a²-4b+4b²)+(a²-b²)-2(a²-4ab+3b²)=a²-4b+4b²+a²-b²-2a²+8ab-6b²=-4b-3b²+8ab=-4(-3)-3(-3)²+8(1/2...
=The square of 4ab-3b
=4*1/2*（-3）-3（-3）*（-3）
=-33
Urgent 200 factorization questions (or integral multiplication and division) and answers
Divide the following into factors
（1）12a3b2－9a2b+3ab;
（2）a（x+y）－（a－b）（x+y）;
（3）121x2－144y2;
（4）4（a－b）2－（x－y）2;
（5）（x－2）2+10（x－2）+25;
（6）a3（x+y）2－4a3c2.
2. Simple calculation
（1）6.42－3.62;
（2）21042－1042
（3）1.42×9－2.32×36
The second chapter decomposes the factor synthesis exercise
1、 Multiple choice questions
1. The deformation from left to right in the following formulas is factorized as ()
(A)(a+3)(a-3)=a2-9 (B)x2+x-5=(x-2)(x+3)+1
(C)a2b+ab2=ab(a+b) (D)x2+1=x(x+ )
2. The correct one in the factorization of the following formulas is ()
(A)-a2+ab-ac= -a(a+b-c) (B)9xyz-6x2y2=3xyz(3-2xy)
(C)3a2x-6bx+3x=3x(a2-2b) (D) xy2+ x2y= xy(x+y)
3. Factorize the polynomial M2 (A-2) + m (2-A) into ()
(A)(a-2)(m2+m) (B)(a-2)(m2-m) (C)m(a-2)(m-1) (D)m(a-2)(m+1)
4. The following polynomials can decompose factors ()
(A)x2-y (B)x2+1 (C)x2+y+y2 (D)x2-4x+4
5. In the following polynomials, the one that can't be decomposed by the complete square formula is ()
(A) (B) (C) (D)
6. If the polynomial 4x2 + 1 is added with a monomial to make it the complete square of an integer, then the added monomial cannot be ()
(A)4x (B)-4x (C)4x4 (D)-4x4
7. The following factorization is wrong ()
(A)15a2+5a=5a(3a+1) (B)-x2-y2= -(x2-y2)= -(x+y)(x-y)
(C)k(x+y)+x+y=(k+1)(x+y) (D)a3-2a2+a=a(a-1)2
8. In the following polynomials ()
(A)-a2+b2 (B)-x2-y2 (C)49x2y2-z2 (D)16m4-25n2p2
9. The following Polynomials: ① 16x5-x; ② (x-1) 2-4 (x-1) + 4; ③ (x + 1) 4-4x (x + 1) + 4x2; ④ - 4x2-1 + 4x
(A)①② (B)②④ (C)③④ (D)②③
10. The square difference of two consecutive odd numbers can always be divided by K, then K is equal to ()
(A) Multiple of 4 (b) 8 (c) 4 or - 4 (d) 8
2、 Fill in the blanks
11. Decomposition factor: m3-4m =
12. Given x + y = 6, xy = 4, then the value of X2Y + XY2 is
13. If the factorization result of XN yn is (x2 + Y2) (x + y) (X-Y), then the value of n is
14. If AX2 + 24x + B = (MX-3) 2, then a =, B =, M =. (photo 15)
15. Observe the figure. According to the relationship between the area of the figure, you can get a formula to decompose the factor without connecting other lines. This formula is
3、 (6 points for each question, 24 points in total)
16. Factorization: (1) - 4x3 + 16x2-26x (2) A2 (x-2a) 2-A (2a-x) 3
（3）56x3yz+14x2y2z－21xy2z2 (4)mn(m－n)－m(n－m)
17. Factorization: (1) 4xy – (x2-4y2) (2) - (2a-b) 2 + 4 (a-b) 2
18. Factorization: (1) - 3ma3 + 6ma2-12ma (2) A2 (X-Y) + B2 (Y-X)
19. Factorization
（1） ； （2） ；
（3） ；
20. Factorization: (1) ax2y2 + 2axy + 2A (2) (x2-6x) 2 + 18 (x2-6x) + 81 (3) - 2x2n-4xn
21. Factorize the following formulas:
（1） ； （2） ； （3） ；
22. Factorization (1); (2);
23. A simple calculation method is used
(1)57.6×1.6+28.8×36.8-14.4×80 (2)39×37-13×34
（3）．13.7
The square difference of two consecutive odd numbers is twice the sum of the two consecutive odd numbers
25. As shown in the figure, in the four corners of a square cardboard with side length of a cm, cut out a square with side length of B (b <) cm, and calculate the remaining area by factorization when a = 13.2 and B = 3.4
26. Factorize the following
（1）
（2） ；
(3) (4)
(5)
(6)
(7) (8)
(9) （10）(x2+y2)2-4x2y2
（12）．x6n+2+2x3n+2+x2 （13）．9(a+1)2(a-1)2-6(a2-1)(b2-1)+(b+1)2(b-1)2
27. Given (4x-2y-1) 2 + = 0, find the value of 4x2y-4x2y2 + XY2
28. Known: a = 10000, B = 9999, find the value of A2 + b2-2ab-6a + 6B + 9
29. Prove that 58-1 solution is divisible by two integers between 20 and 30
30. Write a polynomial, and then decompose it into factors (requirements: the polynomial contains letters M and N, with unlimited coefficients and times, and can be decomposed by extracting common factors first and then formula method)
31. Observe the following formula:
12+(1×2)2+22=9=32
22+(2×3)2+32=49=72
32+(3×4)2+42=169=132
……
What rule do you find? Please use the equation containing n (n is a positive integer) and explain the reason
32. Read the following factorization process and then answer the questions raised:
1+x+x(x+1)+x(x+1)2=(1+x)[1+x+x(x+1)]
=(1+x)2(1+x)
=(1+x)3
(1) The above factorization method is applied times
(2) If we decompose 1 + X + X (x + 1) + X (x + 1) 2 + +X (x + 1) 2004
(3) Decomposition factor: 1 + X + X (x + 1) + X (x + 1) 2 + +X (x + 1) n (n is a positive integer)
34. If a, B and C are the three sides of △ ABC, and satisfy A2 + B2 + C2 AB BC CA = 0. Explore the shape of △ ABC and explain the reason
35. Read the following calculation:
99×99+199=992+2×99+1=（99+1）2=100 2=10 4
1. Calculation:
999×999+1999=____________ =_______________ =_____________ =_____________ ;
9999×9999+19999=__________ =_______________ =______________ =_______________ .
2. Guess 99999999999 × 999999999 + 199999999999 is equal to? Write the calculation process
36. There are several small balls of the same size, one by one, just placed in an equilateral triangle (as shown in Figure 1); put these balls in another way, one by one, just placed in a square (as shown in Figure 2). How many such balls are there at least?
How about 100? That's enough!
Reference materials: 100 factoring problems in junior two_ Baidu Knows
A (A-2) - (a square-2b) = - 8 find (a square + b square / 2) - AB
The solution a (A-2) - (A & # 178; - 2b) = - 8, that is, a & # 178; - 2a-a & # 178; + 2B = - 8 ᦉ A-B = 4 square A & # 178; + B & # 178; - 2Ab = 16 ᦉ A & # 178; + B & # 178; = 16 + 2Ab [(A & # 178; + B & # 178;) / 2] - AB = [(16 + 2Ab) / 2] - AB = 8 + AB AB = 8
A (A-2) - (a square-2b) = - 8 find (a square + b square) / 2-AB?
A (A-2) - (a squared-2b) = - 8
a²-2a-a²+2b=-8
a-b=4
Square on both sides:
a²+b²-2ab=16
Divide both sides by 2:
(a²+b²)/2-ab=8
A (A-2) - (asquare-2b) = - 8 find (asquare + bsquare) & 47; 2-AB? A (A-2) - (a square-2b) = - 8 a ＆ 178; - 2a-a ＆ 178; + 2B = - 8a-b = 4 two sides Square: a ＆ 178; + B ＆ 178; - 2Ab = 16 two sides equally divided by 2: (a ＆ 178; + B ＆ 178;) & 47; 2-AB = 8
Factorization x ^ 3 + 3x ^ 2-4
x^3+3x^2-4
=(x³－x²)＋(4x²－4)
=x²(x－1)＋4(x²－1)
=x²(x－1)＋4(x＋1)(x－1)
=(x－1)(x²＋4x＋4)
=(x－1)(x＋2)²
Square of 9 (a + 2b) - square of 121 (a-3b)