There is a math problem to ask everyone, there is a math problem that can t, help

Method 1: Bring in the method directly, the two methods upstairs are this method, and will not be described in detail.

Method 2: We all know that the difference between f(x+1) and f(x) is that the former is the result of the latter translating one unit to the left, and for the same quadratic function, the difference of the corresponding function value formed by translating one unit to the left (i.e., f(x+1)-f(x)) is unchanged for the same x (as can be seen by drawing the image), and f(x+2) is obtained by f(x+1) moving one unit to the left, and f(x+3) is obtained by moving f(x+2) one unit to the left. The difference is the same every time, ie.

f(x+3) f(x+2) f(x+2) f(x+1) f(x+1)-f(x) (visible from the image).

So. f(x+3)-f(x）＝【f(x+3)－f(x+2)】＋f(x+2)－f(x+1）】＋f(x+1)-f(x）】＝3【f(x+2)－f(x+1）】

Simplified f(x+3)-3f(x+2)+3f(x+1)-f(x)=0

Method 1: Substituting f(x)=ax2+bx+c into the left end of f(x+3)-3f(x+2)+3f(x+1)-f(x)=0, get:

Left end of the equation = a(x+3) 2+b(x+3)+c-(3a(x+2) 2+3b(x+2)+3c) + 3a(x+1) 2+3b(x+1)+3c)-(ax 2+bx+c).

0 = right end of the equation.

Certification. Method 2: Deform f(x+3)-3f(x+2)+3f(x+1)-f(x)=0 to obtain:

3f(x+1)-f(x)= 3f(x+2)- f(x+3)

Left end of the equation = 3a(x+1) 2+3b(x+1)+3c-(ax 2+bx+c).

3ax^2+6ax+3a+3bx+3b+3c-ax^2-bx-c

2ax^2+6ax+3a+2bx+3b+2c

2(ax^2+bx+c)+ 3(2ax+a+b)

2 f(x) +3(2ax+a+b)

Right end of equation = 3a(x+2) 2+3b(x+2)+3c-( a(x+3) 2+b(x+3)+c).

3ax^2+12ax+12a+3bx+6b+3c- ax^2-6ax-9a-bx-3b-c

2 ax^2+6ax+3a+2bx+3b+2c

2(ax^2+bx+c)+ 3(2ax+a+b)

2 f(x) +3(2ax+a+b)

Left end of equation = right end of equation. Certification.

Solution: (1) Class A cost: 183 (yuan);

Class B cost: 70 3 60% = 126 (yuan).

183-126 = 57 (yuan).

Answer: Class A costs a lot of money, and it costs 57 yuan more

2) On the first day of class A, buy x bottles of mineral water, which can be divided into three situations according to the title:

I bought no more than 30 bottles the day before, and more than 50 bottles the next day.

According to the problem: 3x+60% 3 (70-x)=183 solution: x=not in accordance with the title)

Buy no more than 30 bottles the day before, and buy more than 30 bottles but no more than 50 bottles the next day.

According to the problem: 3x+80% 3(70-x)=183 solution: x=25

The number of bottles purchased in two days is more than 30 bottles but not more than 50 bottles According to the question: 80% 3x+80% 3(70-x)=183 This equation has no solution.

To sum up, Class A buys 25 bottles of mineral water on the first day and 45 bottles of mineral water on the second day Answer: Class A buys 25 bottles of mineral water on the first day and 45 bottles of mineral water on the second day

So Zaozhen is bigger than 30 bottles or 50 bottles the next day.

183 3 80% = bottle.

So less than 30 bottles on the first day.

If the stool is made on the first day to buy x bottles, then the second day of the first wheel is 70-x3x+(70-x)*3*

Class 3x+ Class A costs a lot of money, spending 57 yuan more. Buy 25 bottles on the first day of Class A. Buy 45 bottles the next day.

There are 2, 3, and 4 cuts in length, width and height respectively (the length, width and height can be changed at will between the cubes).

The number of surfaces increased by surface area is (2+3+4)*2=18

The total area of 60 blocks is 1*(18+6)=24

Water consumption increased by (5670-5548) 5548=

Raised the key (24250-21650) 21650=

Electricity consumption is growing faster.

1. Proof of the following: it is known that in RT ABC = ACB=45° BAC= BEC=90°, and BEC and BAC are cohypotenuse BC, the point CEAB is concircular and BC is the diameter;

From the properties of the circumferential angle, it can be seen that AEB= ACB=45° and BEC=90°

It can be seen that DEA=45°=AEB, that is, EA bisects DEB;

In RT ABC, BAC=90°, AC=AB, point F is a point on the ray CA, connected BF, over C to do CE BF, and the vertical foot is the point.

CE to AB to G. Verification: ag=af

Proband: Angle FBA = Angle GCA

Recertification of FBA GCA

Set 2 yuan, 3 yuan, 5 yuan ** are a, b, c sheets, then there are.

1) 2a+3b+5c=240 (2) c=2a

2) Replace 1) c+3b+5c=240 i.e. 3b+6c=240 b+2c=80

Both b=80-2c

When c=2 b=80-4=76 a=1 (since c=2a, c can only be even).

c=4 b=80-8=72 a=2

c=6 b=80-12=68 a=3

c=8 b=80-16=64 a=4

c=38 b=80-76=4 a=19

c=40 b=80-80=0 a=20

Because there is no limit to the total number of **, this problem is an indefinite equation with multiple answers. Since the number of sheets of any one type cannot be negative, there are only 20 possible answers.

Solution: Let 2 yuan have x sheets, 5 yuan has 2x sheets, and set 3 yuan has y sheets, so 2*x+5*2x+3y=240 and x, y are integers, that is, 4x+y=80

If there are no other conditions, there is an n-group solution.

Isn't there a shortage of conditions? Or just write one?