Factorization x3-3x2 + X + 1 = 0

X3-3X2+X+1=0
x^3-x^2-2x^2+x+1=0
x^2(x-1)-(2x+1)(x-1)=0
(x-1)(x^2-2x-1)=0

1-2+3-4+5-6+… +1991-1992+1993=______ ．

1-2+3-4+5-6+… +1991-1992+1993 =1+（3-2）+（5-4）+… +(1993-1992), = 1 + [(1993-1) △ 2] × 1, = 1 + 996, = 997; so the answer is: 997

8. Given the ellipse, F1 and F2 are the left and right focuses of the ellipse. Take F1F2 as the edge to make an equilateral triangle. If the ellipse exactly bisects both sides of the equilateral triangle, find the ellipse

Tip: point on ellipse (C / 2, C √ 3 / 2)

The product of the three primes is 42. The three primes are 、、__ ．

42 = 2 × 3 × 7, so the product of the multiplication of the three prime numbers is 42, and the three prime numbers are 2, 3 and 7 respectively

Given 2B + AB + a = 30 (A. B is greater than 0), find the minimum value of y = 1 / ab
THANKS
WHY?

∵ a, b > 0, so the mean inequality can be used to solve
2B+A≥2√2BA
∴AB+2√2AB≤30
2 √ 2Ab ≤ 30-ab, then remove the root sign on both sides
A^B^-68AB+900≥0
The solution is: ab ≥ 50 (rounding off) or ab ≤ 18 (if and only if 2B = a, take the equal sign)
So the minimum value of 1 / AB is 1 / 18, where a = 6 and B = 3

Given the function (x-1) f (x-1 / x + 1) + F (x) = x, where x is not equal to 1, find the analytic expression of the function
...

(x-1) f (x-1 / x + 1) + F (x) = formula one
X is not equal to 1
So, if we use (x + 1) / (x-1) instead of X, we can get,
((x+1)/(x-1)-1)f( ((x+1)/(x-1)+1)/ ((x+1)/(x-1)-1) )+f( (x+1)/(x-1) )= (x+1)/(x-1)
Well organized,
2 / (x-1) f (x) + F ((x + 1) / (x-1)) = (x + 1) / (x-1), multiply both sides by (x-1) to get,
2F (x) + (x-1) f ((x + 1) / (x-1)) = (x + 1) formula 2
You can get formula 2 minus Formula 1,
f(x)=1,
The idea is right, the process is too boring, you can calculate the result, maybe not right

3-2x and (x + 1) / 3 are opposite numbers, what is x equal to?

Solution
3-2x and (x + 1) / 3 are opposite numbers
Then (3-2x) + [(x + 1) / 3] = 0
Multiply both sides by 3 to get:
3(3-2x)+(x+1)=0
That is 9-6x + X + 1 = 0
5x=10
∴x=2

Solution 9. Take the values of the independent variable x and the corresponding dependent variable y of a function as the values of points respectively And In the rectangular coordinate system, describe its pairs
solve
9. Take the values of the independent variable x and the corresponding dependent variable y of a function as the values of points respectively And In the rectangular coordinate system, the corresponding points are described, and the graph composed of all these points is called the integral of the function .
10. The general steps of making function image are as follows , , The graph of a function of degree is a line 11. The coordinates of the intersection of the line y = 3-9x and the X axis are , and the intersection coordinate of Y axis is .
12. The linear function y = 5kx-5k-3, when k = When k, the image passes through the origin Y increases with the increase of X
13. In the linear function y = 2x-5, when x increases from 3 to 4, the value of Y is zero When x increases from - 3 to - 2, the value of Y__ .

9 abscissa, ordinate, function image
10 list of line drawing points
The intersection of 11 and X axis, that is, y = 0 is (1 / 3,0)
The intersection point with y axis and x = 0 is (0,3)
When k = - 35, the image passes through the origin; when k > 0, y increases with the increase of X
13, x from 3 to 4, y from 1 to 3;
X from - 3 to - 2, y from - 11 to - 9

Let t belong to R, find the trajectory equation of the corresponding point Z of the complex z = (T + 1 / T) + (t-1 / T) I, and point out the characteristics of the curve

Complex Z
x=t+1/t (1)
y=t-1/t (2)
(1) Square - (2) square = x ^ 2-y ^ 2 = 4 (x ≥ 2 or X ≤ - 2)
The domain satisfies the trajectory equation and can be saved
The curve is hyperbolic

(7 × 2 / 5) & 178; - 2.4 & 178; (7 × 2 / 5 square - 2.4 Square)
Factorization

7*2/5=2.8²
(7×2/5)²-2.4²
=2.8² -2.4²
=(2.8+2.4)(2.8-2.4)
=5.2*0.4
=2.08

Factorization x3-3x2 + X + 1 = 0