It is known that x + Y-Z = 4 x^2+y^2-z^2=12 x^3+y^3-z^3=34 Find XYZ

It is known that x + Y-Z = 4 x^2+y^2-z^2=12 x^3+y^3-z^3=34 Find XYZ

This is a system of cubic equations with three variables. X + Y-Z = 4 --- > x + y = Z + 4 〉 x ^ 2 + y ^ 2 + 2XY = Z ^ 2 + 8Z + 16 subtracts from the second equation: 2XY = 8Z + 4 〉 xy = 4Z + 2 (x + y) ^ 3 = (Z + 4) ^ 3, then: (x + y) ^ 3 = x ^ 3 + y ^ 3 + 3xy (x + y) = Z ^ 3 + 34 + 3 (4Z + 2) (Z + 4) = (Z + 4) ^ 3 = Z ^ 3 + 64 + 12z ^ 2 + 48Z

When someone runs along the road, take care that every six minutes a bus goes from the back to the front, and every two minutes a bus comes from the opposite. If the speed of the person and the bus remains the same, how many minutes does a bus leave from the bus terminal?
Flood control decided to drain water by boiling water pump in the rain. Assuming that the increase of rainwater per hour is the same, the drainage capacity of each pump is also the same. If one pump can drain the accumulated water in 10 hours and two pumps can drain the accumulated water in 3 hours, how many hours can the three pumps drain the accumulated water?
The master said to his apprentice, "when I was as old as you, you were only 4 years old. In the future, when you are as old as me, I will be 52 years old."?
There is a mixed decimal whose integral part is 200 times of the decimal part. If the decimal point is moved one place to the right, the result is 22.8 times smaller than 11 times of the original integral part

1、4
2、2
3、36、20
4、24.12

The applied problems of mathematical equations in junior middle school
Uncle Wang saved 1000 yuan and 20000 yuan in two ways, and took them out one year later, earning interest of 457.2 yuan. It is known that the sum of the annual interest rate of the two kinds of savings is 2.97%, and the annual interest rate of the two kinds of savings can be calculated.

Let the annual interest rate of the first method be x, and the annual interest rate of the second method be y

A classmate walks along the tram line
When a student walks along the tram line, he sees a tram coming from behind him every six minutes, and a tram coming from the opposite every two minutes. If the speed of the student and the tram is always uniform, then the tram leaves at the starting station every few minutes?

Let the speed of people be x and the speed of cars be y
Then 2x + 2Y = 6y-6x
Y = 2x
Make the distance between two buses s = 2x + 2Y = 6y-6x
So when people walk for a minute: people walk for (1 / 6) s, cars walk for (1 / 3) s
So the departure time interval is: S / [(1 / 3)] s = 3 minutes

The distance between niqiao village and the county is 18 kilometers. Secretary Wang went to the county from the niqiao village committee. When he walked 1.5 kilometers, the correspondent Xiao Zhang found that Secretary Wang had forgotten to bring something, so he ran after him immediately. After Xiao Zhang caught up with Secretary Wang, he immediately returned to the village committee. At this time, Secretary Wang also just arrived at the county. It is known that Xiao Zhang walked 1 kilometers more per hour than Secretary Wang. What are the speeds of secretary Wang and Xiao Zhang?
18-1.5 = 16.5 (km)
16.5 / (1.5 / 1 * 2) = 5.5 (km / h) Secretary Wang
Use 2 2's and 3's as few as possible to form a formula (with brackets). The result is 2005,

Sorry, I only know the first question. When I do the first question, I suggest that I draw a picture first and then do the question. The first formula 18-1.5 = 16.5 (km) is secretary Wang. In the correspondent Xiao Zhang, he found that Secretary Wang forgot to take things to say the distance. In the second formula, 1.5 refers to the distance Xiao Zhang takes more than Secretary Wang, and one of them refers to that Xiao Zhang takes more than Wang

Point to point distance formula Please tell me

For the quadratic trinomial x2-10x + 36, Xiao Cong made the following conclusion: no matter what real number x takes, its value can't be equal to 11. Do you agree with him

We can calculate x = 5

DF (x ^ 2) / DX = 1 / x, find f '(x)

Separation of variables
df(x^2)=dx/x
Two sides integral
f(x^2)=lnx
f(x)=ln√x=1/2lnx
f'(x)=1/(2x)

Any n + 1 vector in n-dimensional vector space must be linearly related. I don't understand this concept. Can anyone explain it to me
It's better to have a specific example to illustrate that I'm so confused by it that there's no one to ask,

Take the simplest example: X1 + x2 + X3 + X4 = 02 * X1 + 3x2 = 0. How many solutions do you have for this system of equations? The answer is that any n + 1 vector in countless n-dimensional vector spaces must be linearly related. That is to say, among the N + 1 n-dimensional vectors, one vector can be found, which can be expressed linearly by the remaining vectors, such as two-dimensional vector [1

Find the differential of this implicit function
(x + y) times of xy = e
Differential dy

xy=e^(x+y)
The derivation of X is y + XY '= e ^ (x + y) (1 + y')
The solution is y '= (e ^ (x + y) - y) / (x-e ^ (x + y)) = (xy-y) / (x-xy)
dy=[(xy-y)/(x-xy)]dx