If the square of x-5x + 6 can be decomposed into the product of two factors, and one factor is X-2, the other is X-2, and the other is mx-m, where m and N are Two unknown constants, please find the value of M, n

If the square of x-5x + 6 can be decomposed into the product of two factors, and one factor is X-2, the other is X-2, and the other is mx-m, where m and N are Two unknown constants, please find the value of M, n

X ^ 2-5x + 6 = (X-2) * (x-3) M = 1 N = 3, please write it clearly when you write it again

Factorization factor (X-Y) (xsquare + XY + ysquare) - XY (Y-X)

（x-y)(x^2+xy+y^2)-xy(y-x)
The original formula = (X-Y) (x ^ 2 + XY + y ^ 2) + XY (X-Y) Changing symbols
=(x-y)(x^2+2xy+y^2) …… Extracting common factors
=（x-y)(x+y)^2

X ^ 2 + 7xy + KY ^ 2-5x + 43y-24 can be decomposed into the product of two linear formulas. Please use the undetermined coefficient method to decompose the original formula and find out the value of K

Let x ^ 2 + 7xy + KY ^ 2-5x + 43y-24 = (x + ay + b) (x + CY + D)
Expand on the right:
x^2+(a+c)xy+acy^2+(b+d)x+(bc+ad)y+bd=x^2+7xy+ky^2-5x+43y-24
The comparison coefficient is as follows
a+c=7 (1)
ac=k (2)
b+d=-5 (3)
bc+ad=43 (4)
bd=-24 (5)
(3) (5) simultaneous equations: B = 3 D = - 8 or B = - 8 d = 3
Substituting (4) to get:
3c-8a=43 (6)
(1) (6) simultaneous solution: a = - 2, C = 9
So: k = AC = - 18
The original factor is decomposed into (x-2y + 3) (x + 9y-8)

X + 2 of X + 1 + (x + 7 of X + 6) - x + 3 of X + 2 - (x + 6 of X + 5) and a few questions to help calculate
1
2. X-6 / 5x + (X-12 / 2x-5) = x-6x + 8 / 7x-10
3. X-1 / 1 + (x + 4x + 1 / 3) + (x + 8x + 1 / 15) +... + (x + 4nx + 4N-1 / 1)
4. Party A and Party B start from a and B at the same time and walk towards each other. After a walks 16 meters, they meet for the first time. Then Party A goes forward to B and returns immediately. Party B also goes forward to a and returns immediately. At 6 meters away from B, they meet for the second time. How many meters is the distance between a and B?
The first few are equations. Fractional equation. Square of X

I didn't understand
The last question is 42 meters
Let the distance be X
First encounter distance ratio 16 / (x-16)
Second encounter distance ratio (x + 6) / (2x-6)
The equation 16 / (x-16) = (x + 6) / (2x-6) is obtained
The solution is x = 0 or 42
42m
What grade questions are interesting

How to calculate x + 1 / 5 + X + 1 / 8 = x + 1 / 6 + X + 1 / 7

General division
(2x+13)/(x²+13x+40)/(2x+13)/(x²+13x+42)
Because X & sup2; + 13X + 40 ≠ X & sup2; + 13X + 42
So 2x + 13 = 0
x=-13/2

x+1/15-x/15=2/1

x+1/15-x/15=2/1
(1-1/15)x=2-1/15
14/15*x=29/15
x=29/14

How to calculate 2 / 1 x = 4 / 1

Move to x = - 1 / 4

When m is a number, the equation x ^ 2 + 2 (m-1) x + 3M ^ 2 = 11
When m is a number, the equation x ^ 2 + 2 (m-1) x + 3M ^ 2 = 11
1. There are two unequal real roots
2. There are two real roots
3. No real root
4. There is a positive root and a negative root
5. There are two positive real roots

x^2+2(m-1)x+3m^2=11
x^2+2(m-1)x+3m^2-11=0
x1=-(m-1)+((m-1)^2-3m^2+11)^0.5=-(m-1)+(m^2-2m+1-3m^2+11)^0.5=-(m-1)+(-2m^2-2m+12)^0.5
x2=-(m-1)-((m-1)^2-3m^2+11)^0.5=-(m-1)-(m^2-2m+1-3m^2+11)^0.5=-(m-1)-(-2m^2-2m+12)^0.5
1. There are two unequal real roots
-2m^2-2m+12>0,(2m+6)(-m+2)>0
2>m>-3
2. There are two equal real roots
-2m^2-2m+12=0,2m^2+2m-12=0,(2m+6)(m-2)=0
M = - 3 or M = 2
3. No real root
-2m^2-2m+120
2>m>-3
5. There are two positive real roots
-2m^2-2m+12>=0,(2m+6)(-m+2)>=0
2>=m>=-3

Solving the mathematical equation x ^ 2 - (3m + 1) x + m (2m + 1) = 0

We just learned that
First, x ^ 2 - (3m + 1) x + m (2m + 1) = 0
The square of x ^ 2-3mx-x + 2m + M = 0
Then we combine the terms with m to get
m（-3x+2m）+x^2-x+1=0
Let (- 3x + 2m) = 0 and x ^ 2-x + 1 = 0 hold at the same time

The equation x / x-1-3m = m / 1-x has an increasing root, and m ≠ 1 / 3

x/x-1-3m=m/1-x
x-3m(x-1)=-m
(3m-1)x=4m
Obviously, increasing roots is X-1 = 0, x = 1
therefore
3m-1=4m
m=-1
[questions are welcome]