Regarding high school mathematics, those who are able to come up and answer

(-1023 2);

f(x)=0;Get root x1, x2....x10, a proportional sequence with the first term 1;

512x2+2*m1*x+1)(512x2+2*m2*x+1)..512x2+2*m5*x+1)=0;

512x2+2*m+1)=0;m is m1 to m5;

x1*x2*x3*x4...x10 = (1 512) * (1 512) * (1 512) * (1 512) * (1 512) = (1 45th of 2);

Let the ratio q; x1*x2*x3*x4...x10 = 45th power of q = (1/45th power of 2); q=1 2;

10 roots and with two roots and for -b a; Gotta :

2*m1/512))+2*m2/512))+2*m3/512))+2*m4/512))+2*m5/512))

10 roots and use the proportional method to calculate; Gotta :

So. -(2*m1/512))+2*m2/512))+2*m3/512))+2*m4/512))+2*m5/512))=1023/512

m1+m2+m3+m4+m5=(-1023 2);

Here's how it works, but I don't see your question clearly, so it's recommended to use a lowercase x for unknowns

The first of the 10 roots of the equation is a proportional sequence of 1.

What do you mean?

The first question is indeed done with special properties, but it must be emphasized that the definition domain is symmetrical with respect to the origin.

Second question: You can also use a property, because f(x+2)= f(x), so the period of this function t=4, f(x)=f(x-4); Since x belongs to [3,7], when x belongs to [3,5], x-4) belongs to [-1,1], it can be substituted for f(x)=f(x-4)=(x-4) 3; When x belongs to [5,7], f(x)=f(x-4)=f[-(x-4)+2]=f(-x+6) is derived from the previous question, and (-x+6) belongs to [-1,1], so it is substituted f(x)=(x+6) 3

In summary, f(x)=(x-4) 3 , x belongs to [3,5] f(x)=(x+6) 3, and x belongs to [5,7].

We know that there is a symmetry property of the function: if f(x)=f(x+a), symmetry with respect to b, then b=(x+x+a) 2, now the problem is that the straight line x=1 is a symmetry axis of the function f(x) image, then f(x) = f(-x+2), i.e. f(-x) = f(x+2) = -f(x), so f(x) is an odd function!

First of all, because x=1 is the axis of symmetry, there is f(x+2)=f(-x)f(x+2)=-f(x) is valid because the domain is defined as symmetry with respect to the origin. The formula used is f(a+x)=f(b-x)

then its axis of symmetry is x=1 2(a+b).

Personally, I understand it because:

x=1, belongs to r, so it is f(x+2) = f(x), as for what you said because x=1 is an axis of symmetry of f(x) images, I don't know, in fact, when doing this kind of problem, you have to write it, we used to train this kind of common this.

With respect to the straight line x=1 axis, then f(1+x) = f(1-x) and f(2+x) = f(-x) = f(x).

So f(x) is an odd function.

The second question is obtained from the properties of the function f(x)=(x-4) 3 [3,5]-(x-6) 3 [5,7].

1.The definition field is: -x 2+2x+3>0

x^2-2x-3<0

x-3)(x+1)<0

i.e. -1=log1 2(4)=-2

That is, the range is [-2,+oo).

3.Since f(x) is a subtraction function, then there is a subtraction interval that is the increasing interval of -x 2+2x+3

And -x 2+2x+3=-(x-1) 2+4, the increasing interval is ( infinity, 1), so the decreasing interval of the function is ( infinity, 1).

For many liberal arts students, mathematics may be a somewhat daunting term, and some students may choose to study liberal arts, advanced mathematics learning methods and experiences because they are not good at mathematics or do not like mathematics very much.

However, mathematics is very important for any liberal arts student, and some people compare mathematics to the lifeblood of liberal arts students, and some people say that mathematics and English determine the level of a liberal arts student to a large extent, which has some truth. Therefore, be sure to do your best to learn math well.

In my opinion, mathematics is actually a very wonderful and interesting subject. As long as you have a pair of eyes that are good at discovering and daring to discover, you will be able to find the charm of mathematics and become interested in it. And interest is the best teacher, if you are both interested in mathematics and determined to work hard to learn mathematics, then how can you not learn well?

For high school students, it belongs to the question of sending points.

Convert sin x to 1-cos x

y=-cos²x+√3cosx+9/4

(cos-√3/2)²+3

When cosx=3 2, x=6, y=3;

When cos=-1, x=,ymin=5 4-3 I wish you happy studying

Let me talk about the solution to the problem.

Convert sinx 2 to 1—cosx 2.

Then the recipe. (You should be, right?) ）

Solve according to cosx's [-1,1].

You don't have to ask for a guide to do it. I don't know how to ask again.

This is because there is tana<0 in front, tanb<0, so a is in the interval (- 2,0), b is in the interval (- 2,0), and there is tan(a+b) in front of >0, so a+b can only be in (- 2), so there is a bottom.

Hello, do you have a title?

Is there any condition in the question that you didn't pay attention to?

sin is in 3 to 2 increments.

2 to 3 4 decreasing.

So the maximum is sin 2=1

The minimum is at the border.

Compare SIN3 and SIN34

So the minimum is sin3 4 = 2 2

θ+π/3∈[π/3,3π/4]

When + 3=3 4, the minimum value of 2 is obtained

When + 3 = 2, the maximum value of 2 is obtained