If the square + 1 of the algebraic formula 4 * a plus a monomial form can form a complete square, then; [1] write all possible monomials in line with the meaning of the problem; [2] write all corresponding complete square forms

If the square + 1 of the algebraic formula 4 * a plus a monomial form can form a complete square, then; [1] write all possible monomials in line with the meaning of the problem; [2] write all corresponding complete square forms

This topic is very good and easy to miss
1）
The monomials that can be added are:
4a
－4a
－4a^2
－1
4a^4
2）
4a^2＋1＋4a＝(2a＋1)^2
4a^2＋1－4a＝(2a－1)^2
4a^2＋1－4a^2＝1^2
4a^2＋1－1＝(2a)^2
4a^2＋1＋4a^4＝(2a^2＋1)^2
Note: a single number is also a monomial

Using 4 × 4 squares, the side length of each small square is 1 unit length, making a square with an area of 10 square units, and then representing the real number on the number axis, root sign 10 and negative root sign 10

Simple. You first need to be able to make root 2 on the number axis (junior high school textbooks have examples). Then cut 2 times root 2 in the horizontal direction, and cut root 2 on the vertical axis to form a rectangle. The diagonal length of the rectangle is root 10. Then cut the square of root 10 * root 10

Requirements: This is the integral part of Chapter 2 of mathematics in Volume 1 of junior high school
1. The radius of a circle is r, which is five times the radius of the other half circle. The sum of the circumference of the two circles is ()
2. If a small square with a side length of a is dug out from the inside of a circle with radius r, the area of the remaining figure is ()
3
(1) (2) the opposite number of the sum of a and X
4. There are a series of algebraic expressions: - x, 2x to the second power, - 3x to the third power, 4x to the fourth power, ··, - 19x to the 19th power, 20x to the 20th power···
(1) Observe its characteristics and narrate the law of this series of algebraic expressions in one's own language;
(2) Write the 2013 algebraic formula;
(3) Write the nth, Nth + 1 algebraic expression
5. The difference between X and y can be expressed as ()

1.、2π[r+(r/5)]=(12/5)πr
2、πR^2-a^2
3、（1）（1/a)+11
(2)-2(a+x)
4、
-x,2x^2,-3x^3,4x^4,-5x^5,…… -19x^19,20x^20……
(1) The rule of the coefficient part of this series is: the absolute value of each coefficient is a natural number arrangement starting from 1, in which the even number term takes a positive sign and the odd number term takes a negative sign; the rule of the letter part is: the first term is x, and the next term is obtained by multiplying the previous term by X
(2) The number of 2013 is - 2013x ^ 2013
(3) The nth number is n * [(- 1) ^ n] * [x ^ n]
The number n + 1 is (n + 1) * [(- 1) ^ (n + 1)] [x ^ (n + 1)
5、x-y

Find the range of function y = 3 [1 / (2-x ^ 2)]
3 is the base. 1 / (2-x ^ 2) is the exponent

2-x^2

A mathematical function problem, to solve the process or ideas
The image of the linear function y = KX + B and the inverse function y = - 2 / X are compared with a (- 1, m) and B (n, - 1)
(1) Write the expression of this first-order function:
(2) Draw a sketch of the function image, and write the value range of X which is a linear function greater than the inverse scale function

Substituting AB into y = - 2 / X
m=-2/(-1)=2
-1=-2/n,n=2
So a (- 1,2), B (2, - 1)
Substituting y = KX + B
2=-k+b
-1=2k+b
So k = - 1, B = 1
y=-x+1
Once a function passes through AB, just connect ab
Y = - 2 / X is in the second and fourth quadrant, which also passes ab,
Draw for yourself
If the first-order function is larger than the inverse scale function, the image of the first-order function is above the inverse scale function
So x

Wang Fei went to the mountain library to borrow books. He walked 3000 meters an hour up the mountain and 5 kilometers an hour back from the original road. He asked for his average speed down the mountain

Average speed = 1 × 2 ÷ (1 / 3 + 1 / 5) = 15 / 4 km / h

Let a be a matrix of order 5, and the square of a is equal to the zero vector, then what is the rank of the adjoint matrix of a?

There are only three cases of the rank of the adjoint matrix of A
When RA = n, ra * = n;
When RA = n-1, ra * = 1;
rA

Is each of plural or singular?

Each of us has a company car
Each boy and each girl works hard
Every one of is also plural

Xinhua bookstore has 3800 new story books, and 800 less literature books than story books. How many of the two kinds of books?

3800-800 + 3800 = 3000 + 3800, = 6800 (copies)

Draw the largest triangle in a rectangle. The area of the triangle is half the area of the rectangle______ (judge right or wrong)

Draw the largest triangle in a rectangle, the bottom of the largest triangle = the length of the rectangle, the height of the largest triangle = the width of the rectangle, the area of the rectangle = length × width, the area of the largest triangle = bottom × height △ 2 = length × width = the area of the rectangle △ 2; so the area of the triangle is half of the area of the rectangle