Solve the maximum value of X1 X2 X7 2010, X1 X2 X3, X2 X3 X4, X3 X4 X5 X1 X2 X3?

x1+x2+x3=2x3, so the problem translates to finding the maximum value of x3.

Substituting x7=x6+x5 into the original formula, we get x1+x2+x3+x4+2x5+2x6=2010

Substituting x6=x5+x4 into the above equation gives x1+x2+x3+3x4+4x5=2010

Substituting x5=x4+x3 into the above equation yields x1+x2+5x3+7x4=2010

Substituting x4=x3+x2 into the above equation gives x1+8x2+12x3=2010

Substituting x1+x2=x3 into the above equation gives 7x2+13x3=2010

i.e. x3=(2010-7x2) 13

If to x1....x7 can take a negative value, then there is no maximum value.

If x1...If x7 is a non-negative number, then when x2=0, the maximum value of x1+x2+x3 is 4020 13

If x1...x7 is a non-negative integer, then there is:

8-7x2=0 (mod 13)

7x2=8 (mod 13)

x2=3 is the minimum positive value for the above equation to hold, and x3=153, i.e., the maximum value of x1+x2+x3 is 306

7 unknowns 6 non-correlated equations, all unknowns can be written as a function of x1 (x2, x3 are fine) and x1+x2+x3 is also a function of x1 since you don't have a limit x1 ......The type of number between x7 (integer?) Positive number? Non-negative? , so there's no question of maximums.

If constraints are added, it is sufficient to convert all constraints into inequality problems.

x4=x1+2x2 x5=x1+2x2+x1+x2=2x1+3x2 x6=x4+x5=3x1+5x2 x7=x5+x6=5x1+8x2 x1+x2+x3+x4+x5+x6+x7 =x1+x2+x1+x2+x1+2x2+2x1+3x2+3x1+5x2+5x1+5x1+8x2 =13x1+20x2=2010 The number of posterior tremor seeps into the world is not necessarily x1=10 x2=94 then x1+x2+x3=208 .

Summary. x1+x2=114, x3+x4=78, x1+x3=42, x2+x4=150, find the value of x1.

The answer is x1=30

There are specific steps to solve the problem, and substituting 30 is indeed true, but it cannot be derived from the problem itself.

For example, if x1 is 40, x2=74, x3=2, x4=76 is also true.

The problem of calculating angles cannot be solved according to the complete solution of the equation, and there is a hidden relationship between angles.

How is 30 calculated?

Can you tell me?

Summary. x^5+x^4+x^3＝-1

It is known that x5+x4+x3=-1 is used to find the value of x3.

Happy New Year, dear, and happy to help you learn whether the number you embody after the x represents multiplication or power.

Dear, I suggest that you provide the following topics, and I will help you analyze and calculate them.

power. x^5+x^4+x^3＝-1

Good. x³＝-1

Is this the answer.

Solution x 5+x 4+x +1 0x 4(x+1)+(x+1)(x -x+1) 0

x 4+x -x+1)(x+1) 0x+1 0x -1 That's the question.

That's why x-1

Dear, this is a process of problem solving.

Your answer to the second ** - a 2013

Let x1=k(x2+x3+x4).

1 3 (x2 + x3 + x4) < = x1< = x2 + x3 + x4 then 1 3< = k< = 1

The original inequality is deformed as.

1+k)^2(x2+x3+x4)^2<=4k(x2+x3+x4)x2x3x4

1+k) 2 4k](x2+x3+x4)<=x2x3x4 (1+k) 2 4k](x2+x3+x4) "Nucleus Jujube=[(1+k) 2 4k](x2+x2+x2)=[1+k) 2 4k]*3x2

x2x3x4>=2*2*x2=4x2

Proof, alteration, dismantling, and erection only need to be proved.

1+k)^2/4k]*3x2<=4x2

1/4(k+1/k+2)*3<=4

Because f(x)=x+1 is a subtractive function on [1, 3,1].

So. 1/4(k+1/k+2)*3<=(1/4)*(1/3+3+2)*3=4

Therefore (x1+x2+x3+x4) 2<=4x1x2x3x4

When x1=2, x2=0, x3=-5, x4=8, 30-(x1+x2+x3+x4)=30-(2+0+(-5)+8)=25, so it is equivalent to splitting 25 1s into 4 parts, and each part has at least 0 1s.

If all 4 parts have at least 1, then c(22,3)=1540;

If all 3 parts have at least 1, and the remaining 1 part is 0, then c(4,3) c(23,2)=1012;

If both parts have at least 1 and the remaining 2 parts are 0, then c(4,2) c(24,1)=144;

If there is at least 1 in part 1 and the remaining part 3 is 0, then it is c(4,3) c(25,0)=4.

A total of 1540 + 2012 + 144 + 4 = 3700 integer solutions.

The upstairs idea is correct, but there is a mistake, using the partition method to insert 3 plates in 12 spaces, and using C(12,3) to ignore the situation where two plates are inserted in one gap. For example, the set of solutions (0,1,2,3) cannot be solved by using this algorithm. That is, if you use a combination, each number will be added by at least 1

So I use this method to solve the problem, and I can eliminate these discards.

First of all, x1, x2, x3, and x4 should be taken to the minimum value of -1, ie

At this point, there are 17-2 = 15 "1s" left. There are 16 empty spaces, using the partition method.

In this case, the combination is used, and since the number added to each number is at least 1, it must satisfy x1 0, x2 1, x3 2, x4 3

So c(15,3)=15*14*13 (3*2*1)=455

Copy the previous "" and do to correct it!!

When x1=2, x2=0, x3=-5, x4=8, 30-(x1+x2+x3+x4)=30-(2+0+(-5)+8)=25, so it is equivalent to splitting 25 1s into 4 parts, and each part has at least 0 1s.

Classification discussion: It is still the partition method (also called the interpolation method). 25 1s, a total of 24 empty in the middle!

If all 4 parts have at least 1, then c(24,3)=2024;

If all 3 parts have at least 1 and the remaining 1 part is 0, then c(4,3) c(24,2)=1104;

If both parts have at least 1 and the remaining 2 parts are 0, then c(4,2) c(24,1)=144;

If there is at least 1 in part 1 and the remaining part 3 is 0, then it is c(4,1) c(24,0)=4.

A total of 2024 + 1104 + 144 + 4 = 3276 integer solutions.

This solution is more intuitive and easier to understand. The solution in the book is a bit winding

Summary. x1+x2+x3 8, how many groups are there in such a positive loss integer x1, x2, x3; In this way, how many groups are there in the natural number solution of the slag mold x1, x2, x3; and satisfies xi i(i 1,2,3), how many groups are there in such a positive integer beam bending solution x1,x2,x3.

I think the answer for you, you see.

The following formula is equal to the first formula multiplied by (1+x4), so the following formula is also equal to 0

When the seven numbers are 20 21 22 23 24 25 26, and the last four numbers can not be smaller, and the spike disadvantage becomes smaller and then satisfied and 159 is not satisfied with the subject of the object, the cover of the family disturbance when x1x2x3 is 19 20 22 or 18 21 22 to obtain the maximum value of 61