Fang Chengjie 1. A plane flies between the two cities with a wind speed of 24 km / h. It takes 2 hours and 50 minutes to fly along the wind and 3 hours to fly against the wind. Seeking no wind is the speed of the plane and the distance between the two cities

Fang Chengjie 1. A plane flies between the two cities with a wind speed of 24 km / h. It takes 2 hours and 50 minutes to fly along the wind and 3 hours to fly against the wind. Seeking no wind is the speed of the plane and the distance between the two cities

2 hours 50 minutes = 17 / 6 hours
Let X be the speed of the aircraft when there is no wind
（x+24)(17/6)=3(x-24)
That is 17 (x + 24) = 18 (x-24)
X = 840 km / h
Range: 3 (840-24) = 2448 km
The solution is obtained as follows: v = - 3 km / h * (24 V = - 3 km / h) * (24 h)
Let the speed of the plane be x and the distance between the two cities be y
y=17/6（x+24）；
y=3（x-24）.
The solution is as follows:
x=840，y=2448
A: the speed of the plane is 840km / h, and the distance between the two cities is 2448km.
Let the equation (24 + x) 170 min = (x-24) 180 min be used to calculate the aircraft speed X
Let X be the speed of the aircraft when there is no wind
（24+x）*17/6=(x-24)*3
X=8
The distance between the two cities is 244-840
First, the common factor of half x ^ 2 - 18 is extracted, and then the square difference formula is used to decompose it
Half x ^ 2-18
=1／2（x²－36）
=1／2(x＋6)(x－6)
If the equation xsquare-3x + 1 / 2 + M = 2 / 2 of X (X-2) has an increasing root, find M
Multiply both sides by X (x-1) (X-2)
x+m(x-2)=2(x-1)
Increasing root means that the denominator is 0
So x = 0, x = 1, x = 2
X=0
x+m(x-2)=2(x-1)
-2m=0
M=0
X=1
x+m(x-2)=2(x-1)
1-m=0
M=1
X=2
x+m(x-2)=2(x-1)
2=2
It's an identity
So m = 0, M = 1
1 / (x ^ 2-3x + 2) + m / X (x-1) = 2 / X (X-2) has increasing roots
Because: x ^ 2-3x + 2 = (X-2) (x-1) = 0, the solution is x = 2 or x = 1
X (x-1) = 0, the solution is: x = 0 or x = 1,
X (X-2) = 0, the solution is: x = 0 or x = 2
1/(x^2-3x+2) + m /x(x-1) = 2/x(x-2)
(x + m (X-2) - 2 (x-1)) / X (X... expansion
1 / (x ^ 2-3x + 2) + m / X (x-1) = 2 / X (X-2) has increasing roots
Because: x ^ 2-3x + 2 = (X-2) (x-1) = 0, the solution is x = 2 or x = 1
X (x-1) = 0, the solution is: x = 0 or x = 1,
X (X-2) = 0, the solution is: x = 0 or x = 2
1/(x^2-3x+2) + m /x(x-1) = 2/x(x-2)
(x+m(x-2)-2(x-1)) /x(x-2)(x-1)=0
(m-1)(x-1) /x(x-2)(x-1)=0
So x ≠ 1, then only if M-1 = 0 or M-1 = 2
The solution is: M = 1 or M = 3
I want a formula for the first day of junior high school
Encounter problem: (a speed + B speed) * time = distance
Pursuit problem: (a speed - B speed) * time = distance
Or (b speed - a speed) * time = distance
Encounter problem: (a speed + B speed) * time = distance
Pursuit problem: (a speed - B speed) * time = distance
(b speed - a speed) * time = distance
1 / 2 x square-18 first extract the common factor, then use the square difference formula to decompose the factor?
1 / 2 x squared-18
=1/2(x²-36)
=1/2(x-6)(x+6)
It is known that the equation x ^ 2-x / k-3x / 1 = 3x-3 / x + 1 has increasing roots. Find the value of increasing roots and K
k/(x^2-x)-1/3x=(x+1)/(3x-3)
3k-(x-1)=x(x+1)
x^2+2x-(3k+1)=0
When k = - 1 / 3, there is increasing root 0
When k = 2 / 3
A. There is a distance of 1000 kilometers between city B. two trains of a and B start from city a and city B at the same time. They meet on the way. Car a arrives at place B 15 hours after meeting, and car B arrives at place a 6 and 2 / 3 hours after meeting. If the speed of car B is 1.5 times that of car a, the speed of car a and car B should be calculated
Let the speed of car a be x and that of car B be 1.5x
15X+20/3×1.5X=1000
X=40
1.5×40=60
If the time taken for two cars to meet is x and the speed of car a is y, then:
（x+15）*y=1000
（x+6+2/3）*1.5y=1000
The solution is y = 40
Then the speed of car B is 60
A complete formula for Factorization of polynomials
1. The method of quoting factor
The coefficient is the greatest common factor, and the letter and term are the ones with the least exponent
2. Formula method
Complete square formula: (a + b) ^ 2 = a ^ 2 + 2Ab + B ^ 2
（a-b）^2=a^2-2ab+b^2
Square difference formula: A ^ 2-B ^ 2 = (a + b) (a-b)
Cubic sum: A ^ 3 + B ^ 3 = (a + b) (a ^ 2-AB + B ^ 2)
Cubic difference formula: A ^ 3 - B ^ 3 = (a-b) (a ^ 2 + AB + B ^ 2) cross multiplication: x ^ 2 + (P + Q) x + PQ = (x + P) (x + Q)
agree!
Agree with the first answer
If the equation x + 1x2 − x − 13X = x + k3x − 3 has an increasing root, find the value of the increasing root and K
If both sides of the equation are multiplied by 3x (x-1), then 3 (x + 1) - (x-1) = x (x + k) is simplified, and X2 + (K-2) x-4 = 0. ∵ the fractional equation has no solution, ∵ x = 1 or (x = 0), x = 1, k = 5, a: the increasing root is 1, K is 5
Jia and Ji both run in a circle with constant familiarity. If they run in the same direction at the same time, they will meet every two minutes. If they run in the same direction, they will meet every six minutes. It is known that Jia is faster than he has run. How many laps has he run in each minute?
Party A and Party B run on the circular road at the same speed. They run in opposite directions once every 2 minutes. They run in the same direction once every 6 minutes. Party A is faster than Party B. how many laps does Party A and Party B run per minute
Let a run x laps per minute and B run y laps per minute
According to the meaning of the title:
2X+2Y=1
6X-6Y=1
The results are as follows
X=1/3,
Y=1/6
That is, a runs 1 / 3 laps per minute, B runs 1 / 6 laps per minute