How to use inequality method to find the range of function? (please give an example)

How to use inequality method to find the range of function? (please give an example)

Inequality method: use basic inequality: a + B ≥ 2 √ AB (a, B ∈ R + (positive real number)) to find the range of function. When using inequality method to find the range, pay attention to the use conditions of mean inequality: "one positive, two definite, three-phase, etc."
e. G. if a semicircular steel plate with a radius of 2m is planned to be cut into a rectangular steel plate, what is the maximum area of the rectangular steel plate?
Using mean inequality ab

How to find the range of Nike function?
When y = x + 1|x, how to determine the value?

It is easy to know after derivation
Y is in X

How to prove the density of real numbers

Obviously, let's take X1 and X2 as real numbers

A and B trains run from two places. Car a runs 75 kilometers per hour, and car B runs 69 kilometers per hour. After car a runs for two hours, car B leaves and goes again
How many kilometers are there when the two cars meet in three hours?

The distance between the two places is 75 × (3 + 2) + 69 × 3 = 582km

The average of the three numbers is 52, and their ratio is 1:2:3. What are the three numbers?

Their sum is 52 × 3 = 156
therefore
A is 156 × 1 ^ (1 + 2 + 3) = 26
B is 156 × 2 ^ (1 + 2 + 3) = 52
C is 156 × 3 (1 + 2 + 3) = 78

The sum of five consecutive even numbers is 130. What are the five consecutive even numbers

Let the third of the five consecutive even numbers be x, then
5x=130
x=26
So. The even number of these five connections is
22 24 26 28 30

The number composed of 5 tens, 3 ones, 7 0.1, 2 0.01 and 9 0.001 is ()

The number composed of 5 tens, 3 ones, 7 0.1, 2 0.01 and 9 0.001 is (53.729)
After reading, I wish you progress!

On a map with a scale of 1:4000000, the distance between a and B is 20cm
Two trains leave from a and B at the same time. A trains 55 kilometers per hour, B trains 45 kilometers per hour. How many hours do the two trains meet

The actual distance between a and B is
20 △ 1 / 4000000 = 8000000cm = 800km
It's necessary for two cars to meet
800 (55 + 45) = 8 hours

Decomposition factor: (B + C-2A) ^ 3 + (c + a-2b) ^ 3 + (a + b-2c) ^ 3
Specific process

Let A-B = D, B-C = e, C-A = F
(b+c-2a)^3+(c+a-2b)^3+(a+b-2c)^3
=(f-d)^3+(d-e)^3+(e-f)^3
=(f-e)((f-d)^2-(f-d)(d-e)+(d-e)^2)-(f-e)^3
=(f-e)((f-d)^2-(f-d)(d-e)+(d-e)^2-(f-e)^2)
=(f-e)((f-d)(f-d-d+e)+(d-e-f+e)(d-e+f-e))
=(f-e)((f-d)(f+e-2d)-(f-d)(f+d-2e))
=(f-e)(f-d)(f+e-2d-f-d+2e)
=(f-e)(f-d)(3e-3d)
=3(f-e)(f-d)(e-d)
=3(c-a-(b-c))(c-a-(a-b))(b-c-(a-b))
=3(2c-a-b)(b+c-2a)(2b-c-a)

There are 450 tons of coal in pile a, pile B and pile C. the weight ratio of pile a to pile B is 5:4. The weight of pile C is 1.5 times that of pile B. how many tons of coal in each pile?

If the pile B coal is x tons, the pile a coal is 5 / 4x tons, and the pile C coal is 1.5x tons
x+5/4x+1.5x =450
The solution is x = 120 tons
Then a: 5 / 4x = 120 * 5 / 4 = 150
C: 1.5x = 120 * 1.5 = 180