A math problem in the first year of junior high school, thinking that he is good at math

Don't be so troublesome as above, just observe and analyze.

The original formula has the 0,1,2,3,4 powers of x.

Since it is a completely flat method, it must be [x 2+(?.]x+constant】 2 form.

Oral arithmetic constant: 1*2*3*4+1=25 The constant obtained by the square is the coefficient of x of 5 simple calculation of the original formula, 2*3*4+1*3*4+1*2*4+1*2*2*3=50

Original = (x 2 + 5x+5) 2

Do you understand? If there is anything you don't understand, we can talk about it.

This solution doesn't have to be so troublesome! Don't come directly to solve this kind of problem, just find the trick, I hope mine can help you!

Original = (x+1)(x+4)*(x+2)(x+3)+1(x 2+5x+4)(x 2+5x+6)+1(x 2+5x+4)[(x 2+5x+4)+2]+1(x +5x+4) 2+2(x 2+5x+4)+1[(x 2+5x+4)+1] 2

x^2+5x+5)^2

You can also do this:

x+1)(x+4)*(x+2)(x+3)+1(x 2+5x+4)(x 2+5x+6)+1(x 2+5x+4)(x 2+5x+6)+1 (x 2+5x=a, that is, (a+4)(a+6), and then calculate.

x^2+5x）^2+10(x^2+5x)+24+1(x^2+5x+5)^2

I thought about it for a long time, and I hope it will be, thank you.

It can be obtained according to the title.

Original = (x+1)*(x+4)*(x+2)*(x+3)+1(x +5x+4)*(x +5x+6)+1, let x +5x+5 =a

a-1)*(a+1)+1

a²-1+1

a i.e. (x 5x+5).

There will be so many people when I type...

I haven't come in yet.

Sweat...

Solution: If the original plan is to make x parts, the time required before taking the new process is x 5 hours, according to the title:

10/5 + x-10+6) / 5(1+60%) =x/5 -32 + x-4)/8= x/5 -3

80+5x-20=8x-120

Solve the equation: x=60

So the original plan was to make 60 parts, and it was originally scheduled to be completed in x 5 = 12 hours.

Set the original plan to do x hours, time y hours.

5y=x6+（x-10)=5*160%*(y-3-10/5)x=60 ,y=12

It's not hard to list the equations.

Column equations, assume.

The original plan was to do how many parts x, and the task was originally scheduled to be completed in y hours.

5y=x5* 3-10/5)=x+6-10

The solution is y=12, x=60

The original plan was to make 60 parts, but it was originally scheduled to be completed in x 5 = 12 hours.

1, (1-3 12) (1 12 + 1 15) = 5 (days) 2, set A x, B y

16x=16y+480

3+5)x=3y+480

Solve for x=78 y=48

3 divided by (1 30 + 1 12-1 15) = 20 (minutes).

1. Set x days to complete the task, according to the title, there is one-twelfth multiplied by three plus parentheses, one-twelfth plus one-fifteenth parentheses, multiplied by x equals 1. Just write the equation according to the description.

2. The velocity of A v1, the velocity of B v2, according to the title, 16v1 = 16v2 + 480;3v2+480=5v1。The drawing is clear.

3. The net water intake per minute is 1/30 plus 1/12 minus 1/15, and dividing 2 3 by this net water intake per minute is the number of minutes required.

Question Supplement Question Answers.

Solution: Let 80% of the brine take x kilograms, then 40% of the brine take (160-x) kilograms.

80%x+40%（160-x）=50%*16080%x+64-40%x=80

40%x=16

x=40160-x=120

Take 40 kg of 80% brine and 120 kg of 40% saline.

The scoring formula is: (number of correct answers - 15) 100 (15 - number of wrong answers) 100 The difference between true and false is 50

So: Team A scores: (18-15) 100 (15-12) 100 (18-12) 50 300 points.

Team B scores: ...10 50 — 500 points.

Team C scores: ...15—9）×100＝..600 points.

Team D scores:...4 50 200 points.

The score is calculated as:

Number of correct answers - 15) * 100 = (15 - number of wrong answers) * 100 = difference between true and false * 50

A (18-12)*50=300

B -10*50=-500

C (15-9)*100=600

Ding 4*50=200

Number of correct answers - 15) * 100 = (15 - number of wrong answers) * 100 = difference between true and false * 50

A (18-12)*50=300

B -10*50=-500

C (15-9)*100=600

Ding 4*50=200

That's it, choose me.

Root number (m 2 root number n).

Root number [a+b 2 root number (axb)], a+b=m, axb=n, a>b].

Root number [(Root number A, root number B)].

Root number A Root number B;

Root number (9-4 root number 5).

Root number [9-2 root number (5x4)], 5+4=9, 5x4=20] = root number [(root number 5-root number 4)].

Root number 5 - root number.

You'd better take a picture of the original question so I can answer it for you.

Because the average water bill is $ per ton, the water used in March must be more than 10 tons, and the water used in March is x tons.

x=14 Mr. Wang used 14 tons of water in March.

Solution: If the investment in project A is 10,000 yuan, the investment in project B is (20-x) yuan.

A x = 15 B 20-x = 20-15 = 50,000 yuan.

。。。Wouldn't it be nice to solve the equation with two formulas in columns, x+y=200000

Assuming that the investment in project A is x0,000, then the investment in project B is (20-x) yuan.

The revenue of Project A is: x*

Project B's revenue is: (20-x)*

The benefits obtained by this enterprise are: the income of project A + the income of project B.

That is: x* solution gets x*

Project A invests 150,000 yuan and Project B invests 50,000 yuan.

It seems to be a problem of chickens and rabbits in the same cage.

Solution: The project has invested yuan.

Project B invested (200,000) yuan.

Solution: =150,000 RMB.

Project A invested 150,000 yuan.

Project B invested $50,000.

If the landlord learns a quadratic equation, you can.

Solution: The project has invested yuan.

Project B invested $y.

y=200，000

Solution: { 150,000. }

y=50，000

Project A invested 150,000 yuan.

Project B invested $50,000.

1.Solution: Let the total rent be y, then.

y=1800(30-x)+1600x+1600[20-(30-x)]+1200(30-x)

79600 = 1800 (30-x) + 1600x + 1600 [20-(30-x)] + 1200 (30-x).

Solution x=28

That is, there are 28 B-type combine harvesters sent to area A.

3.Assuming that it is possible, substitute y=89700

89700=1800(30-x)+1600x+1600[20-(30-x)]+1200(30-x)

If x= is solved, the hypothesis is not true.

Therefore, it is not possible to make the total shipping cost 89,700 yuan.

Happy New Year's Day

Option 1: Type A Type B.

Area A: 2 units, 28 units.

Area B: 18 units, 2 units.

Scheme 2: Type A Type B.

Area A: 1 and 29.

Area B: 19 units, 1 unit.

Scheme 3: Type A Type B.

Area A: 0 units, 30 units.

Area B: 20 units, 0 units.

3.From y 200x+74000, it can be seen that when x takes the maximum value x 30, y max 200 30 + 74000 80000 (yuan) OK?

A type A harvester area A 1800 yuan.

Type B harvester A area 1600 yuan.

A type A harvester area A 1600 yuan.

Type B harvester A area 1200 yuan.

1) If X type B combine harvesters are sent to area A, the type A combine harvester sent to area A is 30-x

Combine harvester B 30-x sent to area B, combined harvester type A sent to area B 20-(30-x) = x-10

The total amount of rent received for 50 combine harvesters in one day.

1800（30-x）+1600x+1600（x-10）+1200（30-x）

74000+200x（0<=1<=30)

2）79600=74000+200x

x=28, so the B-type combine harvester is sent to the tabletop = 28 in area A

3) The function is an incremental function, when x=30, the maximum total rent = 74000 + 200 * 30 = 80000<89700

So it is impossible to make the total shipping cost is 89,700 yuan.

(1)y=1800(30-x)+1600(x-10)+1600x+1200(30-x)

2) Let y=79600 solve the equation.

The above equation is simplified as:

y=200x+74000

Bring in y=79600.

x=28 means 28 B-type combine harvesters sent to area A.

3) This equation is monotonically incremental.

Therefore, when x is maximum, there is a maximum value, because a maximum of 30 harvesters can be sent to place B, so y (maximum profit) = 74000 + 200 * 30 = 80000, so it is impossible.

First, the distribution of **.

Second, the machine arrangement.