If 1 + X + x2 + X3 = 0, find x + x2 + X3 + +The value of X2000

If 1 + X + x2 + X3 = 0, find x + x2 + X3 + +The value of X2000

x+x2+x3+… +x2000=（x+x2+x3+x4）+（x5+x6+x7+x8）+… +（x1997+x1998+x1999+x2000）=x（1+x+x2+x3）+x5（1+x+x2+x3）+… +x1997（1+x+x2+x3）=0．

The values of x ^ 3 + x ^ 2 + X + 1 = 0, x + x ^ 2 + x ^ 3 +... + x ^ 2000 are known

x+x^2+x^3+......+x^2000
=x(1+x+x²+x³)+x^5(1+x+x²+x³)+…… +x^1997(1+x+x²+x³)
=0+0+…… +0
=0

Known 1 + X + x ^ 2 + x ^ 3 + +X ^ 9 = 0 find the value of x ^ 2000 + 1 / x ^ 2000

Every two items are merged, that is, (1 + x) + (1 + x) * x ^ 2 + (1 + x) * x ^ 4 + (1 + x) * x ^ 6 + (1 + x) * x ^ 8 = 0
Extract the common factor (1 + x) to get (1 + x) (1 + x ^ 2 + x ^ 4 + x ^ 6 + x ^ 8) = 0
In the two brackets on the left side of the equation, the second one can't be equal to 0, so only 1 + x = 0, x = - 1
x^2000=1
The result is 2

Given the function f (x) = LNX, G (x) = x ^ 2 / 2
1. Let f (x) = Ag (x) - f (x), (a > 0), if f (x) > 0 is constant, find the value range of real number a
2. If x 1 > x 2 > 0, there is always m [g (x 1) - G (x 2)] > x 1F (x 1) - x 2F (x 2). The range of real number m is obtained

1 , F' (x ) = ax - 1/ x ; ( a>0 ,x >0 )
F '(x )=0 : x =sqrt(1/a)
When x belongs to (0, sqrt (1 / a)), f '(x) < 0;
When x belongs to (sqrt (1 / a), + ∞), f '(x) > 0; therefore, f (x) gets the minimum value at x = sqrt (1 / a)
The results are as follows: a * / 2A - ln (1 / a) > 0; 1 / 2 > ln 1 (/ a); a > (1 / sqrt (E));
2 , m[g(x1)-g(x2)]>x1f(x1)-x2f(x2) >0
It is equivalent to m X1 ^ 2 / 2 - X1 ln X1 > m x2 ^ 2 / 2 - x2 ln x2;
Therefore, as long as H (x) = m x ^ 2 / 2 - x ln X. H (x) satisfies monotonic increasing;
H '(x) is always greater than 0
H '(x) = m x - (1 + ln x) > 0, M > 0
H '(x) = m - 1 / X; H' (x) gets the minimum at x = 1 / m
h '( 1/m ) =1 - ( 1+ ln (1/m ) ) > 0;
ln (1/m ) < 0;
1/m < 1
m > 1;
This is the general idea. I don't know if there is any miscalculation

How many cubic meters is a bottle of oxygen
How many cubic meters of oxygen are commonly used in a steel cylinder?

There are 4-liter, 10 liter and 40 liter cylinders,
How much oxygen can the oxygen bottle hold is calculated by the following formula
(volume * 145) = () l oxygen;

If for any non-zero rational numbers a and B, the definition operation "⊙" is as follows: a ⊙ B = B △ A-1, then what is the result of (- 4) ⊙ 3 ⊙ (- 2)?
If for any non-zero rational numbers a and B, the definition operation ⊙ is as follows: a ⊙ B = B / A-2, then what is the value of (- 6) ⊙ 2? (- 6) ⊙ 2 ⊙ 1?

If for any non-zero rational numbers a and B, the definition operation "⊙ B" is as follows: a ⊙ B = B △ A-1, then the result of (- 4) ⊙ 3 ⊙ (- 2) is 1 / 7,
If for any non-zero rational numbers a and B, the definition operation ⊙ is as follows: a ⊙ B = B / A-2, then the value of (- 6) ⊙ 2 is (- 7 / 3),
(- 6) ⊙ 2 ⊙ 1 is (- 17 / 7)

Detailed formula of sphere area
Given that the radius of a sphere is 2.5 meters, what is the total area of the sphere

The formula of sphere surface area is as follows
S = 4 π R ^ 2 = 4 * 3.14 * 2.5 * 2.5 = 78.54 square meters

How many meters is a light year

15
Answer: liujun427 - Mage Level 12 10-5 17:29
How far is a light year
Light year, a unit of length, refers to the distance that light travels in a year, that is, about 9460 billion kilometers (or 5880 billion miles). More formally, it is defined as: in a Julian year (365.25 days, and 86400 seconds per day), in free space and infinitely far away from any gravitational field or magnetic field, Because the speed of light in vacuum is 299792458 meters per second, one light year is 9460730472580 meters, or about 9.46 meters
Light year is usually used to measure a great distance, such as the distance between the solar system and another star. Light year is not a unit of time. In astronomy, the second gap is a very common unit, which is equal to 3.26 light years
One light year is 63240 astronomical units
The distance of a light year is 946.08 billion km (the speed of light in a vacuum is constant, about 300000 km / s)
Calculation equation: one light year = 365 x 24 x 60 x 60 x 30 W
relevant:
It takes about eight minutes for light to reach the earth from the sun
It is known that the nearest star to the solar system is the nearby star Centaurus, which is 4.22 light years apart
Our galaxy, the Milky way, is about 100000 light-years in diameter
Assuming that there is a spaceship with the speed of light from one end of the galaxy to the other, it will take more than 100000 years. But this is only for the static observer, the journey experienced by the crew is only a few minutes. This is due to the time inflation of the moving clock in special relativity
The visible universe is about 15 billion light-years in diameter

Zu Chongzhi, a great mathematician in ancient China, had calculated the PI between and exactly 1500 years ago, and took it as density ratio and approximate ratio, then ()
A B
C D

About 22 / 7 and 355 / 113 respectively

∫ (x ^ 2-y ^ 2) dydz + (y ^ 2-z ^ 2) dzdx + (Z ^ 2-x ^ 2) DXDY, s is the upper half ellipsoid x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 + Z ^ 2 = 1 (z > = 0)
What about Gauss's formula after ∫ ∫ (x + y + Z) DV = ∫ ∫ ∫ Z DV

Then, because the integral region is symmetric about X and y, the integral for X and Y is 0
∫∫∫（x+y+z）dv=∫∫∫ z dv
=∫zdz∫∫dxdy
=∫(0->1) [z*(πab(1-z^2))]dz
=πab/4
Where π AB (1-z ^ 2) = ∫∫ DXDY is the area of the section of the ellipse corresponding to Z