How many real roots of equation 2x ^ 2-6x / (x-3) = x + 5

If the denominator is multiplied, it is a cubic equation of one variable, and there are three real roots

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1. If x2-3x + 1 = 0, the value of fraction x2 / (x ^ 4 + x2 + 1) is Ask God for help!
2. . = = Lim 1 / (x ^ 2-3x + 2) find the limit value,
3. The limit of ((3x + 1) / (3 + x)) ^ (1 / (x-1)) when x tends to 1
4. If the equation of motion of a body is s = 7T ^ 2-13t + 8, then its instantaneous velocity at t = () is 1 Note: if the interval is | T, t + △ x |, then △ y = 7 △ x ^ 2 + 14T △ x + 7T ^ 2-13t-13 △ x + 8-7t ^ 2 + 13t-8 = 7 △ x ^ 2 + 14T △ x, then △ Y / △ x = 7 △ x + 14T, so 14T = 1, t = 1 / 14. But the answer is 1?
5. A math problem of Liberal Arts in senior two. (Application of derivative) A manufacturer manufactures and sells a kind of beverage in spherical bottles. The manufacturing cost of the bottle is 0.8 π R ^ 2, where R is the radius of the bottle, and the unit is cm. It is known that the manufacturer can make a profit of 0.2 points for every 1ml of beverage sold, and the maximum radius of the bottle that the manufacturer can manufacture is 6cm Q: (1) what is the radius of the bottle to maximize the profit of each bottle? (2) When the bottle radius is large, the profit of each bottle is the smallest? Please write the process, thank you
6. It is known that the derivative of F (x) is 2x ^ 2-4ax-3. If f (x) has and only has one extreme point in (- 1,1), the value range of a is obtained
7. Find the sum of all integer solutions of the system of inequalities 5 ＞ 2 (1 − x) − 13X ≤ 23 − X
8. Solve the system of inequalities x + 1 ＞ 0. X ≤ (X-2 / 3) + 2, and write the largest integer solution of the system of inequalities
9. In the "beautiful Urumqi" activity, a community decided to use 9000 pots of chrysanthemum and 8100 pots of sunflower with a and B gardening styles, a total of 100 flowers were placed in the community. The flowers required for each gardening style are shown in the following table: & nbsp; & nbsp; need chrysanthemum (pot) need sunflower (pot) & nbsp; a shape & nbsp; & nbsp; 100 & nbsp; 60 & nbsp; A B shape & nbsp; 80 & nbsp; Based on the above information, let's set X horticultural models of type A to answer the following questions: (1) please write out the inequalities that meet the meaning of the problem and find out the solution set; (2) if the cost of matching a horticultural model of type A is 600 yuan and that of matching a horticultural model of type B is 800 yuan, try to determine how many of the models of type a can make the cost of the 100 horticultural models the lowest
10. Inequalities and systems of inequalities A rectangular football field is xcm in length and 70m in width. If its perimeter is greater than 350m and its area is less than 7560m2, the value range of X is obtained
11. If the set a {x | x + A / x2-4 = 1} is a single element set, then the value set of a is m= The teacher's answers were 2, - 2, - 17 / 4, but I wrote - 17 / 4 and - 4, X + a divided by the square of x minus 4 equals 1
12. Given a = {(x, y) | x2 + y2-6x-8y + 20 = 0}, B = {(x, y) | kx-y-4k + 3 = 0}, then the number of elements of a ∩ B is () A. 0B. 1C. 2D. 3
13. If M = {y | y = x2 + 1}, n = {y = | y = 3-x2}, then M intersects n =?
14. Set a = {y | X & # 178; + 2x, - 2 ≤ x ≤ 2} B = {x | X & # 178; + 2x-3 ≤ 0} take any element a in set a, then what is the probability that a belongs to B Eager for answers
15. Set a = {y | y = x & # 178; - 1, X ∈ r}, B = {y | y = - 2x & # 178; + 2, X ∈ r}, find a ∩ B Set a = {y | y = x & # 178; - 1, X ∈ r}, B = {y | y = - 2x & # 178; + 2, X ∈ r}, find a ∩ b set P = {y | y = 3x-1, X & gt; 1}, q = {y | y = - 2x & # 178; + 10, X ∈ r}, find P ∩ Q
16. Given the set a = {x │ - 1 ≤ x ≤ 2}, B = {y │ y = 2x-a, a ∈ R, X ∈ a}, C = {Z │ z = x & # 178;, X ∈ a} Is there a real number a so that C is included in B? If it exists, find out the value range of A. if it does not exist, explain the reason.
17. A mathematical problem in the first chapter of compulsory senior one: the square of quadratic function y = ax - 4x + a-3d for any x belongs to R, the value of Y is negative, find the range of A A mathematical problem in the first year of senior high school: the square of quadratic function y = ax-4x + a-3d for any x belongs to R, the value of Y is negative, and the range of a is calculated I'm sorry, there is a mistake in the title. If there is no D, it's a mistake! What is correct is a mathematical problem that must be solved in grade one of senior high school: the square of quadratic function y = ax - 4x + A-3. For any x belongs to R, the value of Y is negative, and the range of a is calculated
18. The equation of line passing through point (5,1) and tangent to circle "x square + y square = 25" is -
19. What is the linear equation passing through the point (- 1,2) and tangent to the square of circle x + the square of y = 5?
20. A mathematical problem about set in grade one of senior high school Set {(x, y) | y = x2-1, | x | less than or equal to 2, X belongs to Z} How to express it by enumeration,