Given 1 + X + x ^ 2 + x ^ 3 = 0, find x + x ^ 2 + x ^ 3 + +The value of x ^ 2000 Well Which one? I made it myself the fastest

Given 1 + X + x ^ 2 + x ^ 3 = 0, find x + x ^ 2 + x ^ 3 + +The value of x ^ 2000 Well Which one? I made it myself the fastest

1 + X + x ^ 2 + x ^ 3 = 0, multiply both sides by X, x + x ^ 2 + x ^ 3 + x ^ 4 = 0, multiply both sides by x ^ 4, x ^ 5 + x ^ 6 + x ^ 7 + x ^ 8 = 0, then multiply x ^ 4, and do this all the time. The last item is x ^ 1997 + x ^ 1998 + x ^ 1999 + x ^ 2000 = 0, so x + x ^ 2 + x ^ 3 + +x^2000 =0...

（1）x²+2x-99=0 （2）（x-1）（x+3）=12

x²+2x-99=0
(x+11)(x-9)=0
x1=-11,x2=9
(x-1)(x+3)=12
x²+2x-3=12
x²+2x-15=0
(x+5)(x-3)=0
x1=-5,x2=3

The perimeter of the rectangle is 22. If the length is reduced by 1 and the width is increased by 2, then the area of the original rectangle is 2______

Let the length and width of the original rectangle be x and Y respectively. According to the meaning of the title, we get x − 1 = y + 22 (x + y) = 22, and the solution is x = 7Y = 4, so the area of the original rectangle is 7 × 4 = 28

In Lin (x tends to 0 +) x ^ n * LNX, why do we say that the limit of x ^ n is 0, while the limit of LNX is negative infinity
How to judge whether it is infinite or infinitesimal

This is very simple. When x approaches 0 +, x ^ n is equal to 0 ^ n, of course 0
When x approaches 0 +, we can know that LNX approaches negative infinity according to its image

It is known that a and B are respectively the middle points of the left and right focus Pb of the ellipse x2 / A2 + Y2 / B2 = 1. Find: 1, the standard equation of the ellipse
It is known that a and B are the left and right focal points of the ellipse x2 / A2 + Y2 / B2 = 1, O is the origin of the coordinate, P (- 1, two-thirds root sign) is on the ellipse, and the intersection point m of line Pb and Y axis is the midpoint of line Pb

The intersection m of line segment Pb and Y axis is the midpoint of line segment Pb, which indicates that the abscissa of point B and P are opposite numbers, equal to 1
That is, C = 1
Then substitute (- 1, two-thirds root sign) into x2 / A2 + Y2 / B2 = 1
Let m = a ^ 2
1/m+0.5/(m-1)=1
Solve M = 2 or M = 0.5 (rounding off)
So the elliptic standard equation x ^ 2 / 2 + y ^ 2 = 1

The sum of six times of a prime number and six times of another prime number is 180. What are the two prime numbers

The sum of two prime numbers is 180 / 6 = 30
So the prime numbers are 11 and 19, or 13 and 17, or 23 and 7

It is known that when x = 6, the inequality loga (x2-2x-15) > loga (x + 13) holds, then the solution set of the inequality is

By substituting x = 6 into the original formula, we can get loga9 > loga19, from which we can know 0

Let the function f (x) = 23x + 5 + Lg3 − 2x3 + 2x, (1) find the domain of definition of function f (x); (2) judge the monotonicity of function f (x) and give the proof; (3) know the inverse function F-1 (x) of function f (x), ask whether the image of function y = F-1 (x) intersects with X axis? If there is, calculate the coordinates of the intersection; if there is no intersection, explain the reason

(1) From 3x + 5 ≠ 0 and 3 − 2x3 + 2x ＞ 0, the solution is x ≠ - 53 and - 32 ＜ x ＜ 32. Take the intersection to get - 32 ＜ x ＜ 32. (2) let μ (x) = 3x + 5, with the increase of X, the function value decreases, so it is a decreasing function in the domain of definition; 3 − 2x3 + 2x = - 1 + 63 + 2x, with the increase of X, the function value decreases, so it is a decreasing function in the domain of definition

It is known that P is a prime number. If P 10 and P 14 are prime numbers, what number will p be?

P + 10, P + 14, right?
If so, P = 3

Is there such a relationship between the distribution function and the marginal density function
Let f (x, y) = f (x) * f (y), then the edge density function of X is f (x), and the edge density function of Y is f (y)?

Yes, but only when x and y are independent of each other!