A primary school mathematics problem, on the proportion of the best equation solution (simple equation) If someone travels 5 kilometers per hour from a to B, he will arrive 4 hours later than the scheduled time. If he travels 7 kilometers per hour, he will arrive 2 hours earlier than the scheduled time

A primary school mathematics problem, on the proportion of the best equation solution (simple equation) If someone travels 5 kilometers per hour from a to B, he will arrive 4 hours later than the scheduled time. If he travels 7 kilometers per hour, he will arrive 2 hours earlier than the scheduled time

Set the scheduled time to x hours
5:7=（x-2):(x+4)
5(x+4)=7(x-2)
5x+5×4=7x-7×2
5x+20=7x-14
x=17
5 × (17 + 4) = 105 (km)
The distance between a and B is 105 km

Solving a quadratic equation of two variables
x^2+500x-125000=0

（x-250）²=187500
X = 250 + 25 √ 3 or 250-25 √ 3

Solving high school equation with mathematics
① How does - 1 - (x ^ 3-2x) = (3x ^ 2-2) (1-x) become (x-1) ^ 2 (2x + 1) = 0
② How does Q ^ 9-q ^ 6-q ^ 3 + 1 = 0 become (Q ^ 3-1) (Q ^ 6-1) = 0
How to change these two equations? Is it based on high school knowledge? Is there any specific formula? How to solve it

① - 1-x ^ 3 + 2x = (3x ^ 2-2) (1-x) - 1-x ^ 3 + 2x = 3x ^ 2-3x ^ 3-2 + 2x sort it out to get 2x ^ 3-3x ^ 2 + 1 = 02x ^ 3-2x ^ 2-x ^ 2 + 1 = 0 (this step is the most critical, split - 3x ^ 2 into - 2x ^ 2-x ^ 2, so you can extract the common factor. This is a very common method, and it's very easy to use. Remember this) 2x ^ 2 (x-1) -

Solving two equation problems
One is 8x = 9x-6, and the other is 4x-3 = 2x + 3

8x-9x=-6
-x=-6
x=6
4x-2x=3+3
2x=6
x=3

T ^ 4-100t ^ 3 + Pt ^ 2 + QT + r = 0, where p, Q and R are nonzero constants

They are all irrational numbers

0.83x=y+z
2.5y=x+z
3.33z=x+y
x+y+z=1

By simultaneous equations 1 and 4, it can be concluded that:
x=1/(0.83+1)
x=0.546
By simultaneous equations 2 and 4, it can be concluded that:
y=1/(2.5+1)
y=0.285
By simultaneous equations 3 and 4, it can be concluded that:
z=1/(3.3+1)
z=0.232
If we take x, y, Z into equation 4, x + y + Z = 1.06 is not equal to 1
All the equations have no solution

1)x+y-z=13 2）x+y=16
y+z-x=-1 y+z=12
z+x-y=3 z+x=10

1)
① The formula 2 is added to get y = 6
① The sum of formula 3 gives x = 8
② The formula 3 is added to get z = 1
So x = 8, y = 6, z = 1
2)
① 2. Add and subtract from 3 to get y = 9
Substituting y = 9 into 1, we get x = 7
Substituting y = 9 into 2, we get z = 3
So x = 7, y = 9, z = 3

1. Party A and Party B start from place a to place B at the same time. Party A drives by himself at a speed of 10km / h, and Party B walks at a speed of 6km / h. When Party A arrives at place B, Party B is 8km away from place B. Q: how long did party a walk? What is the distance between a and B?
2. Some of the same rooms need to be decorated with floor tiles. Four skilled workers can decorate five rooms a day, of which 3 square meters are not decorated. Six junior decoration workers can decorate seven rooms a day, but also install another 5 square meters of floor. It is known that a skilled worker decorates 3 square meters more than a junior worker every day. How large is the area of each room?
3. The price of type a refrigerator sold in shopping malls is 2190 yuan, and the daily power consumption is 1 degree. Although the price of type B refrigerator is 10% higher than that of type a refrigerator, the daily power consumption is 0.55 degree. Now the type a refrigerator is sold at a discount. How much discount should the shopping malls give for the consumers to buy? (calculated according to the usage period of 10 years, 365 days per year, and 0.40 yuan per degree)
4. The cost price of a product sold by a factory is 28 yuan per piece. If it is sold directly from the factory, the price of each product is 35 yuan, and other expenses are 2100 yuan per month. If it is sold by a merchant, the ex factory price is 32 yuan per piece
(1) How many pieces are sold each month under these two sales methods, and the profit is the same?
(2) If the sales reach 1000 pieces per month, which sales method is more profitable?
5. There are 9 tons of milk in a dairy factory. If fresh milk is sold directly in the market, the profit will be 300 yuan per ton. If it is made into yogurt, the profit will be 1200 yuan per ton. If it is made into milk flakes, the profit will be 2000 yuan per ton. The production capacity of the factory is: if it is made into yogurt, it can process 3 tons per day, and if it is made into milk flakes, it can process 1 ton per day, Limited by the temperature, this batch of fresh milk must be sold or processed within 4 days. Therefore, the factory has designed two schemes. One is to make milk flakes as much as possible, and the other is to sell fresh milk directly; the other is to make some milk flakes, and the rest is made into yoghurt, and it is finished within 4 days. Which scheme do you think will make the most profit?

1. A and B start from a to B at the same time. A rides a bicycle at a speed of 10km / h, and B walks at a speed of 6km / h. When a arrives at B, B is 8km away from B. Q: how long did a walk? What is the distance between a and B? Suppose a walked XH. Suppose the distance between a and B is YKM

Come and help me with a multiple choice math problem
In the first 1000 natural numbers, there are 168 prime numbers, so how many combined numbers are there?
830 831 832
Which one? I wonder if 0 should be included?
If 0 is included, 1000-168-1-1 = 830
But the answer is 831. I suspect that there may be mistakes in the answer sometimes. Please help me think about it!

A long time ago, 0 was not a natural number. After a few years, it became a natural number
0 is neither prime nor composite
Prime number is in "all integers larger than 1", except 1 and itself, there is no other divisor. This kind of integer is called prime number or prime number. It can also be said that a prime number has only 1 and its two divisors
A composite number is a "positive integer" which can be divided by other positive integers except 1 and itself
The scope is given in the definition, and 0 is not in the scope of discussion

The solution of equation 2 (4 ＾ x + 4 ＾ - x) - 7 (2 ＾ x + 2 ＾ - x) + 10 = 0 is?
I'm a good boy! -_ -///

The original equation can be transformed into
2[2^2x+2^(-2x)]-7[2^x+2^(-x)]+10=0
Let 2 ^ x = a
The original equation is deformable and can be sorted as (because 2 ^ 2x > 0, the factor can be reduced)
2a^4-7a^3+10a^2-7a+2=0
Easy to observe that 1 is a root, then use the formula method to get
(a-1)^2(2a^2-3a+2)=0
Because 2A ^ 2-3a + 2 is always greater than 0, the equation has only one root, a = 1
If 2 ^ x = 1, then x = 0