![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
A mathematical problem in function and equation We know the equation x & sup2; - (m-2) x-m & sup2 / 4 = 0 about X. if the two real roots X1 and X2 of this equation satisfy | x2 | = | x1 | + 2, find the value of M and the corresponding X1 and x2
The discriminant of the equation = (m-2) ^ 2 + m ^ 2 > 0
So m is any value and the equation has two roots
According to Weida's theorem:
x1+x2=m-2 (1)
x1*x2=-m^2/4
For the square of | x2 | = | x1 | + 2, we get:
(| x2 | - | x1 |) ^ 2 = 4, i.e
x2^2+x1^2-2|x1*x2|=4
(x1+x2)^2-2x1*x2-2*|-m^2/4|=4
(m-2)^2-2*(-m^2/4)-2*(m^2/4)=4
The solution is as follows
M = 0, or M = 4
When m = 0, the equation is x ^ 2 + 2x = 0
So X1 = 0, X2 = - 2
When m = 4, the equation is x ^ 2-2x-4 = 0
So X1 = 1 - √ 5, X2 = 1 + √ 5
On trigonometric function, plane vector, probability, statistics, etc
Let AB be an acute angle, cosa = 4 / 5, Tan (a-b) = 1 / 3, and find the value of tanb
Question 2: the purchase price of each piece of clothing is 40 yuan. If the selling price of each piece is set at 70 yuan, it is estimated that 200 pieces can be sold, and if the selling unit price is reduced by 5 yuan, 50 more pieces can be sold. Question: how many pieces should be purchased? What is the selling price of each piece? What is the maximum profit? What is the maximum profit?
What's the probability of randomly selecting three products from three authentic products and two defective products?
If a line passes through point a (- 2. - 6) and is parallel to the x-axis, then the equation of the line is?
Question 4. Divide 8 students into two groups, 3 students in one group and 5 students in the other group?
If a + B = 4, what is (1 + Tana) multiplied by (1 + tanb)?
1. Cosa = 4 / 5, because it is an acute angle, so Sina = 3 / 5, Tana = 3 / 4tan (a-b) = (Tana tanb) / (1 + tanatanb) = - 1 / 3, so: (3 / 4-tanb) / (1 + 3 / 4tanb) = - 1 / 3 solution: tanb = 13 / 92, unit price reduced x 5 yuan (30-5x) (200 + 50x) = 250 (- x ^ 2 + 2x + 24) = 250 [- (x-1) ^ 2 + 25]
2 times 2012-9
[(28 + 0.5) + 1.3 times 5] divided by 1.4
2 and 7 / 20 divided by [5 and 3 / 5-4.5 times (20% + 1 / 3)]
It's easy. It's easy
[9 and 2012 / 2011 - (8-2012 / 1)] divided by 2 times 2 / 1 = (9 + 2011 / 2012-8 + 1 / 2012) / / 2 × 1 / 2 = (1 + 1) / / 2 × 1 / 2 = 1 / 2 [(28 + 0.5) + 1.3 times 5] divided by 1.4 = (28.5 + 6.5) / / 1.4 = 35 △ 1.4 = 252 and 20 / 7 divided by [5 and 5 / 3-4.5 times (20% + 3 / 1)] = 47 / 2
RELATED INFORMATIONS
- 1. It's not difficult, 1. When measuring the average speed of 100m for a student, the timekeeper starts to count the time when he hears the starting gun at the end. The result shows that the student's score is 10s. If the speed in the air is 340m / s, what is the actual average speed of 100m 2. There are two rolls of thin copper wire, one of which is marked with the words "(refer to the mark in the figure) = 0.3mm", the other roll of label falls off, and the diameter is unknown. If there is no copper length measuring tool, and you are given two identical pencils, can you measure the diameter of the copper wire more accurately? (refer to the mark in the figure) is a symbol similar to the Chinese character The most important thing is to look at the first question, and the second one is OK without looking at it!
- 2. A, C, B went fishing, a fished 11, B fished 7, C fished 7. Later, a tourist came, and four people roasted all the fish. Finally, the tourist paid 6 yuan. How can the money be divided reasonably?
- 3. Three math problems (one practical problem, 1、 Practical questions: 1. An iron block with a volume of 100 cubic centimeters is completely immersed in a rectangular container with a length of 5 cm, a width of 4 cm and a height of 20 cm. At this time, the water surface height is 12 cm. If the iron block is fished out, what is the water surface height? 1. Weld a cube with 24 cm long wire. The surface area of the cube is () A. 48 square centimeter b.36 square centimeter c.24 square centimeter 2. Saw a cuboid 12 cm in length, 9 cm in width and 5 cm in height into a cube of the same size with 3 cm in edge length. You can saw () at most A.98 B.45 C.12
- 4. 2 math problems = w= A cylindrical wood is 10 meters long. After it is cut into two cylinders, the surface area increases by 0.4 square meters. What is the volume of the original wood? 2. A cone-shaped wheat pile with a bottom radius of 2 meters and 8 meters. If the wheat is put into a cylindrical grain bin with a height of 4 meters and is just full, how many square meters is the bottom area of the cylinder?
- 5. Calculation and application problems in Grade 6 Winter vacation homework requires 50 calculation questions in Grade 6 with 3 or more steps. Application questions are not only for graphics, but also need 20 questions in one step. The questions must be in the second semester of grade 5 and grade 6. The simpler the questions, the better! ~ ~ but it can't be too simple! ~ ~ ~ which kind-hearted person can help me find the questions... Because I'm a novice... So I offer a reward of 15 points... Help me~~~
- 6. 1. The farmyard uses the traditional stone mill as a food processing tool to attract tourists? 2. In some places above 70 ° n, there is no night for about two months in a year, which accounts for half of the whole year___ %Due to the high latitude, the average sunshine time of Stockholm in July is about 75% of that of a day____ Hours
- 7. Have I learned all the basic training of mathematics in Volume 2 of grade 6 of primary school
- 8. The sixth grade first semester people's education press exercise book mathematics question 64 pages Today! The efficiency of the drug
- 9. Primary school sixth grade mathematics small exercise book unit 9 homework 2 second big question ground seven small questions
- 10. Break through in Mathematics (fill in the blanks) Explanation with "*" to solve the problem 1. Fill in "" or "=" in brackets (11/21*6/7)*42( )11/21*42 (1/7+1/8)*56( )1/7+1/8*56 *2. There are 540 boys in Yuhong primary school, 2 / 9 more girls than boys, and () more girls than boys *3. From 3 / 4 tons of cement, 2 / 5 tons are transported, and () tons are transported; from 3 / 4 tons, 2 / 5 tons are transported, and () tons are left
- 11. The function f (x) = x3-x2 + x2 + 14 is known. It is proved that there exists x0 ∈ (0,12) such that f (x0) = x0
- 12. A and B drinks with the same kind of fruits and vegetables but different concentrations, a drink weighs 40 kg and B drink weighs 60 kg. Now pour out a part from each of the two drinks, and the weight of the poured out part is the same, and then mix the poured out part of each drink with the rest of the other drink. If the fruit and vegetable concentrations of the mixed two drinks are the same, then pour out a part from each drink Out of the same weight is___ Kilogram
- 13. After practice, Ding Ding wrote 15 more words per minute than before. It is known that Ding Ding now writes twice as many words per minute as before. How many words per minute did he write?
- 14. A and B two cars from AB two places at the same time, opposite, two car speed and distance between the two places When the two cars meet in the middle of the way, the distance between the two cars is 8:7. After the meeting, the two cars immediately return to their respective starting point. At this time, the handlebar speed of car a is increased by 25%, while the speed of car B remains unchanged. When car a returns to a, car B is still four fifths of an hour away from place B (1) The speed of car B is () km (2) How many km is the distance between the two places?
- 15. The speed ratio of a and B is 5:4 when they meet in two hours. The distance between AB and a is 270km. How many kilometers do a and B travel each hour?
- 16. B and B leave from ab at the same time. When they meet, the distance ratio of B and B is 6:5. After meeting, B is 11 kilometers faster than before, As a result, the two vehicles arrive at the destination at the same time. It is known that Party B has a total of 9 hours Last year, there were 600 red goldfish and black goldfish in the pond. This year, a quarter of the red goldfish swam away, while the number of black goldfish increased by a third. Therefore, there are 534 red goldfish and black goldfish in the pond this year. How many of them are red goldfish?
- 17. The two trains leave from a and B and meet at 48km from the midpoint after 4 o'clock. The speed of the slow train is five seventh of that of the fast train. What are the speeds of the fast train and the slow train?
- 18. How many kilometers is the distance between the two stations known to be 4 kilometers?
- 19. The fast and slow trains start from both places at the same time and run in opposite directions. They meet at 4km from the midpoint. The speed of the slow train is 6 / 7 of that of the fast train. How about the distance between the two places?
- 20. Party A and Party B walk from ab at the same time. When Party A walks at the midpoint of two places, Party B still has 1 / 3 of the distance from the midpoint of the whole journey. What is the speed ratio of Party A and Party B?