Math problems please see Supplement 5, Math problems please see Supplement .

1. (x 2+1) (x 2-1) squared difference formula.

x 2+1)(x+1)(x-1) squared difference formula.

2. xy(9x 2-1) extracts the common factor xy

xy(1-3x)(1+3x) squared difference formula.

3. A 3[(x+y) 2-4c 2] extracts the formula of the square difference of the common factor a 3a 3(x+y+2c)(x+y-2c).

a2（x－y）＋b2（y－x）

4a^2(x-y)-b^2(x-y)

x-y)(2a+b)(2a-b)

a－b）2－（a＋b）2

2(a-b)]^2-(a+b)^2

2(a-b)+(a+b)][2(a-b)-(a+b)](3a-b)(a-2b)

6）（x2＋x＋1）2－1

x 2+x+1-1)(x 2+x+1+1) squared difference formula.

x^2+x)(x^2+x+2)

x(x+1)(x^2+x+2)

When factoring, observe the formula, extract the formula first, and then see if you can apply the learned formula (squared difference, perfect squared formula) to decompose. Hope it helps

In simple operations, the multiplicative distribution rate is used the most, followed by the subtractive nature.

Solution: If the candidate answers question x correctly, then the candidate answers the wrong question (26-x).

8x-（26-x)×5=0

13 x=26×5

x=10

Suppose the candidate answers question x correctly, then the answer is wrong (26-x).

So. 8x+（-5）（26-x）= 0

Solution. x = 10

26 - x = 16

Answer: This candidate answered 10 questions correctly and answered 16 questions incorrectly.

Solution: If you answer question x correctly, you answer question (26-x) incorrectly.

8x-5(26-x)=0

8x-130+5x=0

13x=130x=10

Answer: I answered 10 questions correctly and answered 16 questions incorrectly.

Answered question x correctly.

8x-5(26-x)=0

8x+5x=130

13x=130

x = 10 answered incorrectly = 26-10 = 16 questions.

In this quarter, Factory A plans to produce x sets of 112 x+110 (36000-x)=40000x=20000 of a certain model of automobile engine

110 -1) (36000-20000)=1600In this quarter, Factory A overproduced 2,400 automobile engines of a certain modelIn this quarter, Factory B overproduced 1,600 automobile engines of a certain model.

A is 12% over, B is 10% over, if both factories are 10% over, then 36000+36000*;

In fact, the first super is 12%, so 40000-39600=400 is 2% of the first ultra

400 2% get A actual production volume of 20000 units, it exceeds the quota by 20000 * 12% 2400 units.

The total excess of the two factories is 40,000 - 36,000 = 4,000 units, and the excess of plant B is 4,000 - 2,400 = 1,600 units.

From x 2 + y 2 = a 2 + 2 a-3 to know a 2 + 2 a-3 > 0, the solution is a<-3 or a>1

x 2+y 2=a 2+2a-3 can now be seen as the center of the circle at the origin, and the radius is under the root number (a 2+2a-3).

Then the straight line is tangent to the circle, so the distance from the center of the circle to the straight line is equal to the radius, and the equation can be 2a-1|Root number 2 = root number under (a 2 + 2a-3).Square can get:

2a 2-8a+7=0, solution: a=(4-root number 2) 2, the other root is rounded.

When x0 is the minimum value, x0=- (a +2a-3) y0=0 When y0 is the minimum value, x0=0, y0=- (a +2a-3)x0+y0=- (a +2a-3)=2a-13a -6a+4=0

There seems to be a problem.

Profit: 50-29 = 21 yuan Loss: 50 + 21 + 29 = 100 Total: loss 100-24 = 76 yuan.

1. Set up 5x people in A and 3x people in B.

5x-22)：(3x+22)=3：4

4(5x-22)=3(3x+22)

20x-88=9x+66

11x=154

x=14, so A has 70 people and B has 42 people.

2. Take the width as the diameter to obtain the circle, that is, the largest circle, the radius = 4 2 = 2 dm 3, the sector area = the area of the circle * (the central angle of the circle 360) = * the perimeter of the sector = two sides + arc length.

where the side length = radius arc length = circumference * (central angle 360) = 2 r 6 = 2 *

The circumference is in meters.

If you need a value, please let us know.

1. Solution: (1) Let y=kx+b(k≠0), then there is:

b = 2992000k + b = 235, the solution is k = -

4125b=299，y=-4125x+299；

2) When x = 1200, y = -4125 1200 + 299 = grams cubic meters).

Answer: The oxygen content of the air at the top of the mountain is about gram cubic meters 2, this question mainly examines the application of the analytical formula of the primary function of the method of undetermined coefficients, and the correct analytical formula of the primary function is the key to solving the problem

1) At an altitude of 0 meters, the oxygen content of the air is about 299 grams of cubic meters; At an altitude of 2000 meters, the oxygen content of the air is about 235 grams of cubic meters, which can be obtained by substituting the analytical formula;

2) According to the altitude of a mountain is 1200 meters, substitute the analytical formula in (1) and find it

The first question, set up a and B two workshops are 5x, 3x, (5x-22) :(3x+22) = 3:4

4(5x-22)=3(3x+22)

20x-88=9x+66

11x=154

x=145x=5*14=70,3x=3*14=42, so there are 70 people in workshop A and 42 people in workshop B.

The second question is that the circle can only be cut in a square, so the maximum diameter can only be 4 decimeters wide in a rectangle.

So the radius of the circle is 2 decimeters.