If the solution of equation x2-5x + 6 = 0 and equation x2-x-2 = 0 is m, then the number of elements in M is () A. 1B. 2C. 3D. 4

∵ the solution of equation x2-5x + 6 = 0 is X1 = 2, X2 = 3 ∪ the set of solution of equation x2-5x + 6 = 0 is {2, 3}. Similarly, the set of solution of equation x2-x-2 = 0 is {- 1, 2}. Therefore, the set M = {2, 3} ∪ {- 1, 2} = {- 1, 2, 3} has three elements in total

If the set M = {x | MX + X + 1 = 0} has only one element, we can find the value range of real number M
If the set M = {x | MX + X + 1 = 0} has only one element, find the value range of real number M

1. When m = 0, x = - 1 m has only one element. When m ≠ 0, △ = 1-4m = 0, M = 1 / 4, the univariate quadratic equation is changed to: x ^ 2 + 4x + 4 = 0, x = - 2 m has only one element. In conclusion, M = 0 or M = 1 / 4, I hope it can help you. Please adopt the teacher's solution

(1) the number of real roots and the sum of real roots of the equation 2x Λ 3-6x Λ 2 + 3 = 0 are known

Because complex roots must appear in pairs, the number of real roots of cubic equation can only be one or three. If two roots are found, then the equation has three roots. Let f (x) = 2x ^ 3-6x ^ 2 + 3f (0) = 3, f (1) = - 1, then the equation has one root in (0,1), f (3) = 54-54 + 3 > 0, so the equation has one root in (1,3)

Given the set a = {x | X & # 178; + 3x-18 ＞ 0}, B = {x | (x-k) · (x-k-1 ≤ 0)}, if a intersects B and is not equal to an empty set, the value range of K is obtained

A={z|x3} ,B={x|K≤x≤k+1}
A∩B≠∅,
So k > 3 or K + 1

The known set a = {x ^ 2-3x-18 > 0}, B = {(x-k) (x-k-1) ≤ 0}
1. If a ∩ B = an empty set, find the value range of K
2. If a ∩ B = B, find the value range of K

Solve inequality a to get a = {X6}
The graph opening of the corresponding expression of B set is upward, and - k > - k-1
If a ∩ B = empty set, then - k-1 ≥ - 3 and - K ≤ 6
The solution is - 6 ≤ K ≤ 2
If a ∩ B = B, then - K6
The solution is K3
You must choose me!

8x²-1=（3x-1）（2x+3）

8x²-1=（3x-1）（2x+3）
8x^2-1=6x^2+7x-3
2x^2-7x+2=0
x^2-7x/2=-1
(x-7/4)^2=33/16
X-7 / 4 = soil √ 33 / 4
x1=7/4+√33/4 x2=7/4-√33/4 .

There are several problems to solve, | X & # 178; - 3x | 4, | X / 1 + X | X / 1 + X
It's a process. It's urgent!

|x²-3x|＞4
X & # 178; - 3x > 4 or X & # 178; - 3x4
x²-3x-4>0
(x-4)(x+1)>0
x> 4 or X

It is known that the square of (M's Square-1) x-mx + 8 = 0 is a one variable linear equation about X. find the value of formula 199 (M + x) (x-2m) + 22m

The square of ∵ (M & # 178; - 1) x - MX + 8 = 0 is a linear equation of one variable with respect to X
∴m²-1=0
m₁=1
m₂=-1
∴x₁=8
x₂=-8
When m = 1, x = 8: 199 (M + x) (x-2m) = 199 × (1 + 8) × (8-2) = 199 × 9 × 6 = 10746
When m = - 1, x = - 8: 199 (M + x) (x-2m) = 199 × (- 1-8) × (- 8 + 2) = 199 × (- 9) ± (- 6) = 10746

They are all solved by linear equations of one variable
1. A large cylindrical cup with an inner diameter of 12 cm pours water into a small cylindrical cup with an inner diameter of 6 cm and an inner height of 12 cm. After the water is filled, how many centimeters does the water height in the large cup drop?
2. If the water consumption of a user does not exceed 20 cubic meters per month, the charge will be 1.2 yuan. If the water consumption exceeds 20 cubic meters, the charge will be 2 cm. If the average water charge of a user is 1.5 yuan per cubic centimeter, how many centimeters of water does the user share?

1. Is the inner diameter a radius or a diameter? I calculate it according to the diameter
6 ^ 2 * x = 3 ^ 2 * 12;
So x = 3
2. The main unit is cubic centimeter, right?
Let X be the extra cubic centimeter
(20 × 1.2 + 2 × x) / (20 + x) = 1.5 (all money / total volume = average water charge)
So x = 12
So the total is 20 + x = 32

Please solve these two mathematical problems with a linear equation of one variable
A township is rich in bamboo resources. An enterprise has acquired 52.5 tons of bamboo. According to the market information, if the bamboo is sold directly, it can make a profit of 100 yuan per ton. If the bamboo is rough processed, it can process 8 tons per day, and it can make a profit of 1000 yuan per ton. If the bamboo is fine processed, it can process 0.5 tons per day, and it can make a profit of 5000 yuan per ton, And we must sell all the bamboo in one month (30 days)
(1) Bamboo will be all rough processing after sale
(2) After finishing for 30 days, the bamboo that can be processed in the future will be sold directly in the market
Q: is there a third plan, which is to finish some moso bamboo and rough the rest, and finish it within 30 days? If so, the profit after sales will be calculated; if not, please explain the reason
Xingsheng printing and dyeing factory produces a certain product, the ex factory price of each product is 50 yuan, and the cost price is 25 yuan. In the production process, 0.5 cubic meters of sewage is discharged for each product produced. Therefore, in order to purify the environment, the factory designs two schemes for sewage treatment and is ready to implement them
Scheme 1: the factory sewage is purified and then discharged. The raw material cost for each cubic meter of sewage treatment is 2 yuan, and the monthly sewage equipment loss cost is 30000 yuan
Plan 2: the sewage will be discharged to the sewage treatment plant for unified treatment, and 14 yuan will be paid for each cubic meter of sewage
Q: as a factory director, what kind of sewage treatment scheme should you choose on the premise of not polluting the environment and saving money? Please explain it by calculation

1. Roughing X days, finishing 30-x days
8x +0.5*(30-x)=52.5
The solution is x = 5
2. How much waste water is produced every month
X cubic meters of wastewater are treated every month
The first scheme costs 30000 + 2x per month
The second option costs 14x per month
Which is bigger by subtracting the two

If the solution of equation x2-5x + 6 = 0 and equation x2-x-2 = 0 is m, then the number of elements in M is () A. 1B. 2C. 3D. 4