Fill in 2,4,6,8 in the appropriate box according to the requirements, and only fill in one number in each box without repetition. Thank you very much

Can you fill in the six numbers 1, 2, 3, 4, 5 and 6 in the box below? (can't be used repeatedly) mouth + mouth = mouth + mouth = mouth + mouth
Can you fill in the six numbers 1, 2, 3, 4, 5 and 6 in the box below
Mouth + mouth = mouth + mouth = mouth + mouth

1+6=2+5=3+4

Put nine numbers 1-9 into the box (without omission or repetition), so that the sum of the three numbers on each horizontal, vertical and oblique line is equal to 15

Is the derivative of F (x) = (x ^ 2 + 1) (2x ^ 2 + 8x-5) added or multiplied first?

f'(x)=(x^2+1)'(2x^2+8x-5)+(x^2+1)(2x^2+8x-5)'
=2x*(2x^2+8x-5)+(x^2+1)(4x+8)
=4x^3+16x^2-10x+4x^3+8x^2+4x+8
=The derivative of 8x ^ 3 + 24x ^ 2-6x + 8 uses the multiplication rule first

On the derivation of ordinary least square method
According to the first order condition of minimization, the partial derivatives of α and β are obtained and made zero
Please write down the whole derivation process

Let f = ∑ (YT - α - β XT) & sup2; F α′ = - 2 ∑ (YT - α - β XT) = - 2 [∑ yt-t α - β Σ XT] = 0f β′ = - 2 ∑ XT (YT - α - β XT) = - 2 [∑ xtyt - (∑ XT) α - β Σ (XT) & amp; sup2;] = 0t α + β Σ XT = ∑ YT

Derivation,
Given the function f (x) = the third power of X - the second power of X + ax + B
(1) When a = negative 1, find the monotone increasing interval of function f (x)

Then f (x) = x ^ 3-x ^ 2-x + B
So f '(x) = 3x ^ 2-2x-1
Let f '(x) > 0, the solution is x1
So the monotone increasing interval of F (x) is
（-∞,-1/3）,（1,+∞）
Hope to help you, I use a mobile phone, can not receive follow-up, if you have any questions, please send me a message~

Derivation of function 2x ^ 3-5ax ^ 2 + 4A ^ 2x + 1

(2x^3-5ax^2+4a^2x+1 )'
=6x^2-10ax+4a^2

The practical significance of imaginary numbers
What is it? For example, what is the practical significance of "radical - 2" in science?

Most people are most familiar with two kinds of numbers, namely positive number (+ 5,
5) and negative numbers (- 5, - 17. 5)
In ancient times, it was used to deal with the problems of 3-5
It seems impossible to subtract five apples from three. However, in the middle ages
However, the businessman of the company has clearly realized the concept of debt. "Please give me five apples
Yes, but I only have three apples, so I owe you two apples. "
This is equivalent to saying: (+ 3) - (+ 5) = (- 2)
Positive and negative numbers can be multiplied by each other according to some strict rules
The product of a positive number is positive. The product of a positive number multiplied by a negative number is negative,
The product of a negative number multiplied by a negative number is positive
Therefore, (+ 1) × (+ 1) = (+ 1);
（＋1）×（－1）＝（－1）；
（－1）×（－1）＝（＋1）.
Now suppose we ask ourselves: what number will multiply by itself to get + 1
What is the square root of + 1 in mathematical language?
There are two answers to this question. One is + 1, because (+ 1)
X (+ 1) = (+ 1); the other answer is - 1, because (- 1)
A mathematician uses √ ￣ (+ 1) = ± 1 to calculate
(Note: (+ 1) under the root)
Now let's further raise the question: what is the square root of - 1
How many?
We feel a bit embarrassed about this question. The answer is not + 1, because
The self multiplication of + 1 is + 1, and the answer is not - 1, because the self multiplication of - 1 is the same
Of course, (+ 1) × (- 1) = (- 1), but this is
Multiplication of two different numbers, not self multiplication of one
In this way, we can create a number and give it a special symbol,
Let's say 1, and give it the following definition: 1 is the result of self multiplication
The number of - 1, i.e. (1) × (1) = (- 1)
When it was first put forward, mathematicians called this kind of number "imaginary number", just because
This kind of number doesn't exist in the number system they are used to
The point is not more illusory than the ordinary "real number"
Some strictly restricted properties, and like real numbers, are easy to handle
However, it is precisely because mathematicians feel that this kind of number is somewhat illusory, so they give it to mathematicians
This number has a special symbol "I" (imaginary)
The imaginary number is written as (+ I), the negative imaginary number is written as (- I), and the + 1 is regarded as
Is a positive real number, and (- 1) is regarded as a negative real number
To say √￣ (- 1) = ± I
The real number system can correspond to the imaginary number system completely,
We can have - 17.32, + 3 / 10 and other real numbers
Imaginary numbers such as + 5I, - 17.32i, + 3I / 10, etc
We can even draw a system of imaginary numbers when drawing
Let's say you use a straight line with zero as the midpoint to represent a positive real number
System, then, on one side of 0 is a positive real number, on the other side of 0
It is negative real number
In this way, when you pass through point 0, you make another line that intersects the line at right angles
Then you can represent the imaginary number system along the second straight line
The number on one side of the line 0 is positive imaginary, and the number on the other side of the line 0 is negative imaginary
In this way, by using these two kinds of number systems at the same time, we can get the result on this plane
Some numbers are expressed, such as (+ 2) + (+ 3I) or
These numbers are complex numbers
Mathematicians and physicists have found that all the points on a plane are the same number
It's very useful for word systems to connect with each other. If there's no imaginary number, it's very useful
We can't do that

Why is there an imaginary number? What is the definition of an imaginary number?

Numbers are always on the horizontal axis of the number axis, that is, the number on the X axis can be expressed as a real number. The number falling outside the X axis can not be expressed as a distance to the origin. The number expressed by distance plus orientation is an imaginary number
Imaginary numbers are meaningless, but because scientific research needs to express some special algorithms, imaginary numbers are more important

A simplification of imaginary numbers
Z = 2 + 3I is one of the roots of the polynomial Z ^ 4-5z ^ 3 + 18z ^ 2-17z + 13 = 0
thank you!

Because Z ^ 4-5z ^ 3 + 18z ^ 2-17z + 13 = 0 is a real coefficient equation, and z = 2 + 3I is a root, so z = 2-3i must be a root. So (z-2-3i) (Z-2 + 3I) = Z ^ 2-4z + 13 must be a factor of Z ^ 4-5z ^ 3 + 18z ^ 2-17z + 13

Fill in 2,4,6,8 in the appropriate box according to the requirements, and only fill in one number in each box without repetition. Thank you very much