a²（a+1)-2(a²-2a+4） Find (2-1) (2 + 1) (2 & sup2; + 1) (2 ^ 4 + 1) (2 ^ 32 + 1) + 1

a²（a+1)-2(a²-2a+4） Find (2-1) (2 + 1) (2 & sup2; + 1) (2 ^ 4 + 1) (2 ^ 32 + 1) + 1

1. Original formula = a ^ 3 + A ^ 2-2a ^ 2 + 4a-8 = a ^ 3-A ^ 2 + 4a-8 = a ^ 2 (A-2) + 4 (A-2) = (A-2) (a ^ 2 + 4) 2. Original formula = (2 & sup2; - 1) (2 & sup2; + 1) (2 ^ 4 + 1) (2^32+1)+1=(2^4-1)(2^4+1) …… (2 ^ 32 + 1) + 1 = 2 ^ 64-1 + 1 = 2 ^ 642 are 2 / 4 / 8 / 6 / 2 /

Proposition and theorem
Of the following propositions, the false one is______
A. A quadrilateral with two diagonals bisecting each other is a parallelogram
B. Two quadrilaterals with equal diagonals are rectangles
C. Two rectangles whose diagonals are perpendicular to each other are squares
D. Two diamonds with equal diagonals are squares
In the following propositions, which are true propositions and which are false propositions, counter examples are given for false propositions
1. In the same plane, two lines parallel to the same line are parallel
2. If the two sides of the two corners are parallel to each other, then the two corners must be equal

In the following propositions, the false proposition is B a. the quadrilateral whose two diagonals are equally divided is a parallelogram B. the quadrilateral whose two diagonals are equal is a rectangle C. the rectangle whose two diagonals are perpendicular to each other is a square D. the diamond whose two diagonals are equal is a square

1. Point out whether the following propositions are true propositions or false propositions. If they are true propositions, please prove them by logical reasoning. If they are false propositions, please give counter examples
(1) The complements of equal angles are equal;
(2) The sum of the inner angles of the polygon is 180 degrees
2. Rewrite the following propositions into the form of "if, then." and judge whether they are true or false. If they are false, give a counter example
(1) The opposite sides of parallelogram are equal;
(2) The sum of the two acute angles is greater than the obtuse angle;
(3) An isosceles triangle with an angle of 60 ° is an equilateral triangle;
(4) In the same plane, two lines parallel to the same line are parallel to each other;
(5) In the same plane, two lines perpendicular to the same line are parallel to each other

1. (1) true
Angle a = ∠ B,
180 angle a = 180 - B
(2) . false
Rectangle 360
two
If a polygon is a parallelogram, its opposite sides are equal
If there are two acute angles added, then their sum must be greater than the obtuse angle
If an isosceles triangle has an internal angle of 60 degrees, it is an equilateral triangle
In the same plane, if two lines are parallel to the same line, then the two lines are parallel to each other
In If two lines are perpendicular to the same line, they are parallel to each other

The relation between theorem and proposition

Proposition, definition, theorem, axiom, inference
Proposition: a sentence used to judge a thing is called a proposition. A proposition consists of a proposition and a conclusion. A proposition is a known matter, and a conclusion is a matter derived from a known matter. A proposition can often be written as "if. Then..." If the proposition is true, the conclusion must be true. If the proposition is true, the conclusion cannot be guaranteed. If the proposition is false, the conclusion must be true
Definition: a precise and brief description of the essential characteristics of a thing or the connotation and extension of a concept
In order to communicate with each other, people must have a common understanding of some names and terms. Therefore, it is necessary to describe the meaning of names and terms and make clear provisions, that is, to give their definitions
Theorem: a proposition or formula, such as a geometric theorem, that has been proved to be correct and can be used as a principle or law
Generally, it is the initial proposition of a deductive system. Such propositions do not need other propositions to prove in the system, and they are the basic propositions to deduce other propositions in the system
All theorems are true propositions. For example, the vertex angles are equal; two lines are parallel, and the apposition angles are equal; the apposition angles are equal, and two lines are parallel; and so on
Axiom: ① after a long time of repeated human practice, we all agree that there is no need to further prove the proposition, such as: if a = B, B = C, then a = C. ② the correct truth recognized by most people in society
Corollary: generally, it is the supplement and perfection of the theorem (of course, it must be true proposition)

The concept and image of higher one function
(x) = x, G (x) = (2n + 1) root (2n + 1 power of x) (n belongs to n)
Is it the same function?

The second floor is right
G (x) in X

The average number of a and B is 32, and 3 / 5 of a is equal to the number already counted

Let a be X,
3X/5=32*2-X
8X/5=64
X=40
A is 40

Application of linear algebraic matrix and determinant
A is an M × n-dimensional matrix, B is an n × m-dimensional matrix. When m > N, it is proved that | ab | = 0

First, AB is a square matrix of M * M
So to prove that | ab | = 0, we only need to prove that there is a non-zero m-dimensional vector x such that ABX = 0
But this is obvious, because B is n × m dimension matrix, M > N, so BX = 0 has non-zero solution x0
So abx0 = A0 = 0

It takes six minutes for Party A to process a part, five minutes for Party B and four minutes for Party C. now 370 parts need to be processed and three people are required to complete them in the same time. How many parts should each person be assigned?

The work efficiency ratio of a, B and C is: 16:15:14 = 10:12:15, 10 + 12 + 15 = 37, the number of parts to be produced by a is 370 × 1037 = 100, the number of parts to be produced by B is 370 × 1237 = 120, and the number of parts to be produced by C is 370 × 1537 = 150. A: A should allocate 100, B 120 and C 150

7X*3=5X*3+42
Don't just write the results,

7X*3=5X*3+42
7X*3-5X*3=42
X*3*(7-5)=42
X*3*2=42
6X=42
X=7

There are 85 tons of grain in granary A and 75 tons in granary B. the ratio of grain tons in granary A and granary B is 7 to 9. How many tons of grain should be transferred from granary a to granary B?

(85-x):(75+x)=7:9
x=15
15 tons of grain should be transferred from granary a to granary B