It is known that if one root of the equation x2 + (A-1) x + (A-2) = 0 is smaller than 1, then the value range of a is smaller If one of the roots of equation x2 + (A-1) x + (A-2) = 0 is smaller than 1 and one of the roots is larger than 1, then the value range of a is larger

It is known that if one root of the equation x2 + (A-1) x + (A-2) = 0 is smaller than 1, then the value range of a is smaller If one of the roots of equation x2 + (A-1) x + (A-2) = 0 is smaller than 1 and one of the roots is larger than 1, then the value range of a is larger

Let the equation x2 + (A-1) x + (A-2) = 0 be x1, x2,
One root is smaller than one, and one root is larger than one,
x2+(a-1)x+(a-2)=0
(
cross multiplication
1 a-2
1 1
_____
1*1+1*(a-2)=1+a-2=a-1
)
(x+a-2)(x+1)=0
x1=2-a,x2=-1,
Because x2 = - 11,
a

Given that a is a root of the equation x2-x-1 = 0, then the value of a4-3a-2 is______ ．

Substituting x = a into the equation, a2-a-1 = 0, that is, A2 = a + 1, a4-3a-2 = (A2) 2-3a-2 = (a + 1) 2-3a-2 = a2-a-1 = 0

A mathematical equation problem
On a straight road, two cars go in the same direction. At the beginning, car a is 4km in front of car B. the speed of car a is 45km / h, and that of car B is 60km / h. then one minute before car B catches up with car a, the distance between the two cars is () M

Let car B catch up with car a after t hours, then car B runs 60t km and car a runs 45t km. The equation is 60t-45t = 4. The solution of the equation is t = 4 / 15 hours, that is, it takes car B 4 / 15 hours to catch up with car A. 1 minute = 1 / 60 hours, so car B runs 60 * [(4 / 15) -

It takes 9 hours for a car to go from a to B and return to A. It takes 100 kilometers per hour to go and 80 kilometers per hour to return. The distance between the two places is? Km

It's 100 kilometers per hour to go and 80 kilometers per hour to return
The ratio of the speed of going back is 80:100 = 4:5
It took 9 (4 + 5) × 4 = 4 hours to go
The distance between the two places is 100 × 4 = 400 km

In RT △ ABC, ∠ C = 90 °∠ a = 30 ° a = 10 is C=____ b=____

According to the meaning of the title, △ ABC is RT △ and ∠ C = 90 °∠ a = 30 °,
So a: B: C = 1: √ 3:2
When a = 10, B = 10 √ 3, C = 20
Pro, I hope I can help you. Best wishes to you

The distance between station a and station B is 592km, and station a and station B depart from each other at the same time. Car a travels 40km per hour, and the speed of one car is 15% slower than that of car a
How many hours later will the two cars meet?

Vehicle B speed = 40 × (1-15%) = 34 (km / h)
Encounter time = 592 ÷ (40 + 34) = 8 (hours)

The length of the three sides of the unequal triangle ABC is an integer ABC, and the third side C is obtained when a ^ 2 + B ^ 2-4a-6b + 13 = 0

A correspondent rides a motorcycle to deliver the documents within the prescribed time. His speed is 36km per hour. As a result, he arrives 20 minutes earlier. If he is 30km per hour, he will be 12 minutes late. What is the prescribed time? What is the distance?
Use binary linear equations

Suppose: the specified time is x and the distance is y,
According to the meaning of the question, the equation is as follows:
36*（x-20）=y
30*（x+12）=y
The solution of the equations is: x = 180 minutes, y = 5760 km

Let X be a positive real number m, the quadratic function f (x) has the maximum value 4. And the minimum value of the quadratic function g (x) is 3, and G (m) = 11, f (x) + G (x) = x ^ 2 + 4x + 3. Find the analytic expressions of F (x) and G (x)

According to the meaning of the question, when x is m, f (m) = 4, G (m) = 11
From FX + Gx = x ^ 2 + 4x + 3, we can get x ^ 2 + 4x + 3 = 11 + 4 = 15, M = - 6 or 2, rounding off
Let FX = ax ^ 2 + BX + C, then GX = (1-A) x ^ 2 + (4-b) x + 3-c
And because x is m, it has a maximum, so B / - 2A = M = 24ac-b ^ 2 / 4A = 4
After simplification, 4A + 4 = C, B = - 4A
From the minimum value of GX is 3, 4 (1-A) (3-C) - (4-b) ^ 2 / 4 (1-A) = 3
By substituting the above two formulas into the above formula, we can get a = - 1, then B = 4, C = 0
We can get FX = - x ^ 2 + 4x

For a batch of goods, a car can transport one eighth of it at a time, and how much of it can be transported four times? If this batch of goods weighs 116 tons, how many tons can be transported four times?
The formula, and why it's written like this,

4 times = 1 / 8 × 4 = 1 / 2
4 times = 116 × 1 / 2 = 58 tons
Do not understand can ask, help please adopt, thank you!