Given the complete set u = R, a = {X / x ^ 2 > 4}, B = {X / 3-x / x + 1 > o}, find a ∩ (cub), Cu (a ∩ b), (CUA) ∩ (cub)

Given the complete set u = R, a = {X / x ^ 2 > 4}, B = {X / 3-x / x + 1 > o}, find a ∩ (cub), Cu (a ∩ b), (CUA) ∩ (cub)

From x ^ 2 > 4, we can get x > 2 or x2 or XO
When x + 1 > 0, i.e. x > - 1, there is a solution of 3-x > 0 to get X
A = {x | x > 2 or X
Let u = {1,2,3,4,5,6,7,8}, a = {3,4,5}, B = {4,7,8}, find CUA, cub, (CUA) ∩ (cub), (CUA) ∪ (cub), Cu (a ∪ b), Cu (a ∩ b)
CuA=｛1,2,6,7,8｝
CuB=｛1,2,3,5,6｝
(CuA)∩(CuB)=｛1,2,6｝
(CuA)∪(CuB)=｛1,2,3,5,6,7,8｝
Cu(A∪B)=｛1,2,6｝
Cu(A∩B)=｛1,2,3,5,6,7,8｝
Verify that Cu (a ∪ b) = CUA ∩ cub, Cu (a ∩ b) = CUA ∪ cub
Only the first and the second can be obtained
For any x belonging to Cu (a ∪ b), then x does not belong to a ∪ B, then x does not belong to a and X does not belong to B, then x belongs to CUA, and X belongs to cub
X belongs to CUA ∩ cub, so Cu (a ∪ b) is a subset of CUA ∩ cub
For any y belongs to CUA ∩ cub, then y belongs to CUA and Y belongs to cub, then y does not belong to a and Y does not belong to B, then y does not belong to a ∪ B, so y belongs to Cu (a ∪ b), so CUA ∩ cub is a subset of Cu (a ∪ b)
So CUA ∩ cub = Cu (a ∪ b)
Draw a picture to show the correctness of the algebraic identity (2a-b) (a + 2b) = 2A & sup2; + 3ab-2b & sup2
First, draw a rectangle of length 2a and width a, then subtract B from the length and add 2 to the width to get the area of the figure. The result is obvious
Ask some questions about factorization
(1) A factor of the polynomial 2x & # 178; - xy-15y & # 178; is
（A）2x-5y （B）x-3y (C)x+3y (D)x-5y
(2) Factoring in real numbers
（1）x²+6x+8
（2）4x²-13x²+9
（3）3x²+4xy-y²
（4）（x²-2x）² -7（x²-2x）+12
(1) A factor of polynomial 2x & # 178; - xy-15y & # 178; is B (a) 2x-5y (b) x-3y (c) x + 3Y (d) x-5y (2) decomposes the factor (1) x & # 178; + 6x + 8 = (x + 2) (x + 4) (2) 4x & # 178; - 13X & # 178; + 9 = 9-9x & # 178; = 9 (1-x & # 178;) = 9 (1 + X # 178;) = 9 (1 + X # 178;) = 9 (1 + X # 178;)
1.B (2x+5y)(x-3y)
2.(1) (X+2)(X+4)
(2) (4X-9)(X-1)
(3) Wrong title
（4）（x^2-2x-4)(x^2-2x-3)
Draw a picture to show the correctness of the algebraic identity (2a-b) (a + 2b) = the square of 2A + the square of 3ab-2b
First, draw a rectangle of length 2a and width a, then subtract B from the length and add 2 to the width, and get the area of the figure. The result is obvious
(1)-49/y^2+16/x^2=
(2)48-3t^2=
(3)x-14x+49=
(4)a-6a^2b^3+9a^3b^5=
(5)(a^2+b^2)-4a^2b^2=
（1）（7/Y+4/X)(-7/Y+4/X)
(2) 3(4-3T)(4+3T)
(3)(X-7)(X-7)
(4)A(3AB^2-1)(3AB^2-1)
(5)(A^2-B^2)(A^2-B^2)
——Draw a picture to show the correctness of the algebraic identity (2a + b) (a + 2b) = the square of 2A + 5ab + 2B
Calculate the area of each small piece, then add up the area and calculate the total area directly
1.4A & # 178; - 12ab + 9b & # 178; (writing process)
2.1 + X + quarter X & # 178; (writing process)
3.2mn-m & # 178; - N & # 178; (writing process)
4. (X & # 178; + 1) &# 178; - 4x & # 178; (writing process)
5.4-12 (X-Y) + 9 (X-Y) & 178; (writing process)
6. (x + 2) (x + 6) + X & # 178; - 4 (writing process)
(writing process) (2a) (writing process) (2a) (writing process) (2a) (writing process) (2a) (writing process) (2a) (writing process) (2a) (writing process) (2a) (writing process) (2a) (writing process) (2a) (writing process) (2a) (writing process) (2a; (writing process) (2a) (writing process) (2a) (2x2x2x2ax3b + (3b) (3b) (3b) (writing process) (2a-3b) (writing process) (2a-3b) (writing process) (writing process) (writing process) (writing process) (writing process) (writing process) 1 + X + X + 1 / 4x + 1 / 4x4x / 4x; (writing process) (writing process) (writing process) (writing process) (2a) (2a) (writing process) (2a) (writing process) (writing process) (2a) (writing process) (2a) (writing process) (writing process) (writing process) (2a) (writing process) (2a) (2a) (writing process) (writing process) (writing process) (writing process) (writing process) (2a) (2a) (writing process) (writing process; (writing process) (2a) (writing process) (writing process) (writing process; (writing process) (2a) (writing process) (writing process; (writing process) (2a) (2a) (and
1. =（2a）²+2（2a）*（3b）+（3b）²=（2a+3b）²
2. =（x/2）²+2*1*（x/2）+1²=（1+x/2）²
3. =-（m²+2mn+n²）=-（m+n）²
4. = (X & # 178; + 1 + 2x) * (X & # 178; + 1-2x) = (x-1)... Expand
1. =（2a）²+2（2a）*（3b）+（3b）²=（2a+3b）²
2. =（x/2）²+2*1*（x/2）+1²=（1+x/2）²
3. =-（m²+2mn+n²）=-（m+n）²
4. =（x²+1+2x）*（x²+1-2x）²=（x-1）²（x+1）²
5. =2²-2*2*3（x-y）+[3（x-y）]²=（3x-3y-2）²
6. =2x²+8x+8=2（x²+4x+4）²=2（x+2）²
In fact, except for step 4 and step 6, the rest should be achieved in one step
It's unnecessary to write in such detail. Put it away
1. 4a²-12ab+9b²=（2a-3b)^2
2. 1+x+1/4x^2=(1+1/2x)^2
3. 2mn-m²-n²=-(m²-2mn+n²)=-(m-n)^2
4. (X & # 178; + 1) & # 178; - 4x & # 178; = (x ^ 2 + 1 + 2x) (x ^ 2 + 1-2x) = (x + 1) ^ 2 (x-1) ^... Expand
1. 4a²-12ab+9b²=（2a-3b)^2
2. 1+x+1/4x^2=(1+1/2x)^2
3. 2mn-m²-n²=-(m²-2mn+n²)=-(m-n)^2
4. (x²+1）²-4x²=(x^2+1+2x)(x^2+1-2x)=(x+1)^2(x-1)^2
5. 4-12（x-y）+9（x-y）²=[2-3(x+y)]^2
6. (x + 2) (x + 6) + X & # 178; - 4 = x & # 178; + 8x + 12 + X & # 178; - 4 = 2x & # 178; + 8x + 8 = 2 (X & # 178; + 4x + 4) = 2 (x + 2) ^ 2
1.4a²-12ab+9b²=(2a)²-2*2*3ab+(3b)²
=(2a+3b)²
2.1 + X + quarter X & # 178; = 1 & # 178; + 2 * 1 * 1x / 2 + (1x / 2) &# 178;
=(1+x/2)²
3.. 2mn-m & # 178; - N & # 178; = - (M & # 178; - 2Mn + n &... Expansion
1.4a²-12ab+9b²=(2a)²-2*2*3ab+(3b)²
=(2a+3b)²
2.1 + X + quarter X & # 178; = 1 & # 178; + 2 * 1 * 1x / 2 + (1x / 2) &# 178;
=(1+x/2)²
3..2mn-m²-n²=-(m²-2mn+n²)=-(m-n)²
4..（x²+1）²-4x²=.（x²+1）²-(2x)²
=(x²+1+2x)(.（x²+1-2x)=(x+1)²(x-1)²
5.4-12（x-y）+9（x-y）²=2²-2*2*3(x-y)+[3(x-y)]²
=[(2-3(x-y)}²=(2-3x+3y)²
6.（x+2）（x+6）+x²-4=6.（x+2）（x+6）+(x+2)(x-2)
=(x+2)[(x+6)+(x-2)}=(z+2)(2X+4)
=2 (x + 2) (x + 2) = 2 (x + 2) &
Draw a picture to show the correctness of the algebraic identity (2a-b) (a + 2b) = 2A + 3ab-2b
First draw a rectangle, length 2a, width a, then length minus B, width plus 2B, then the area of this figure is (2a-b) (a + 2b) 2A + 3ab-2b, which is the area of small figure. So (2a-b) (a + 2b) = 2A + 3ab-2b is right