Factorization in complex number: x ^ 3-1

Factorization in complex number: x ^ 3-1

x^3-1 =（x-1)(x²＋x＋1）=(x-1)[x＋（1＋√3i）/2][x＋（1－√3i）/2]

How to factorize x ^ 2 + 4 in complex number?

First of all, solve the equation x ^ 2 + 4 = 0 in the complex range, find X1 = 2I, X2 = - 2I, then x ^ 2 + 4 = (x + 2I) (x-2i)

How to type the quadratic root of mathematical symbol with keyboard?

√
Open Microsoft ABC and click the keyboard with the left key
Right click to select the mathematical symbol
You can see it
Or Microsoft ABC
When typing in Chinese, you can see the mathematical symbols by typing v1

If a line segment AB with a length of 2011 length units is placed on the number axis, it can cover up to integer points; if point a is coincident with the point representing - 1000, and point B is on the right side of point a, then the sum of the numbers represented by all the points covered by line segment AB is

If a line segment AB of 2011 length units is placed on the number axis, it can cover up to 2012 integer points;
If point a is coincident with the point representing - 1000, and point B is on the right side of point a, then the sum of the numbers represented by all the points covered by line AB is
2011-1000=1011
=-1000-999-.-1+0+1+2+...+1000+1001+.+1011
=1001+1002+.+1011
=(1001+1011)×11÷2
=2012×11÷2
=1006×11
=11066

The perimeter of a square cloth is 40 decimeters. How many square decimeters is the area of this square cloth? How many square meters is it

Given that the sum and difference of the polynomials 2x ^ 2 + my-12 and NX ^ 2-3y + 6 do not contain x, y, find the value of M + N + Mn

Original solution = 2x ^ 2 + my-12 - (NX ^ 2-3y + 6)
=2x^2+my-12-nx^2+3y-6
∵ excluding x ^ 2 items
∴2x^2-nx^2=0
∴2-n=0
∴n=2
And ∵ does not contain y term
∴my+3y=0
∴m+3=0
∴m=-3
∴m+n+mn=-3+2+(-3)×2
=-3+2+(-6)
=-1+(-6)
=-7

What is the sum of all the natural numbers 1, 2 and 3.999?
It's the sum of numbers. Don't add 1 to 999~
For example, the sum of 10 and 11 is 1 + 0 + 1 + 1 = 3

According to your algorithm, it should be 12600
99=1+2+...+9+1+0+1+1...+9+8+9+9=810
100~199=910
200 ~ 299 = 1010, and so on. If you add up, you get 12600
You must give it to me. It's been a long time

A passenger car and a freight car, respectively, travel from Party A and Party B to each other at the same time and meet in 4 hours. If the passenger car runs for 3 hours and the freight car runs for 2 hours,
The two cars are still 30 / 11 away from each other, and it takes several hours for the bus to complete the whole journey

Because the bus takes three hours and the truck takes two hours, the interval is 11 / 30, so the bus takes three hours and the truck takes two hours, and the interval is 19 / 30
So the bus runs for 6 hours and the truck runs for 4 hours, 38 / 30
And because the van had been on the whole journey for four hours
So the bus went 38 / 30 - 1 = 4 / 15 in two hours
One hour row 4 / 15 △ 2 = 2 / 15
So the whole journey takes 1 △ 2 / 15 = 15 / 2 = 7.5 hours
If you don't understand, please hi me
Happy study

The maximum value of function y = x3-x2-x + 1 on closed interval [- 1,1]

Wait for me to calculate

X - (3-1) ≤ x + 2 solution inequality! X-5 / 2 + 1 ＞ x-3 / 1x-2 ＜ 1-5 / 1X X - (3x-1) ≤ x + 2

x-(3-1)≤x+2
x - 2 ≤ x+2
X is all real numbers
x-5/2+1＞x-3
x-3/2＞x-3
X is all real numbers
x/3 - 2 ＜1- x/5
8x/15 < 3
8x < 45
x < 45/8
The title of this question is not clear?
x-(3x-1)≤x+2
x-3x +1 ≤ x +2
- x ≤ 1
x ≥ -1