For X ∈ R, the values of quadratic function f (x) = x ^ 2-4ax + 2A + 30 (a ∈ R) are all nonnegative numbers, and the range of roots of X / (a + 3) = | A-1 | + 1 is obtained

For X ∈ R, the values of quadratic function f (x) = x ^ 2-4ax + 2A + 30 (a ∈ R) are all nonnegative numbers, and the range of roots of X / (a + 3) = | A-1 | + 1 is obtained

f(x)=x^2-4ax+2a+30
=(x-2a)^2-4a^2+2a+30
To make the value of all real numbers x, f (x) non negative real numbers
The discriminant = 0
2a^2-a-15

It is known that for any real number x, the value of quadratic function f (x) = x2-4ax + 2A + 12 (a ∈ R) is nonnegative. The range of function g (a) = (a + 1) (| A-1 | + 2) is obtained

According to the meaning of the problem, we can see that △ = 16a2-4 (2a + 12) ≤ 0, the solution is - 32 ≤ a ≤ 2, when 1 ≤ a ≤ 2, G (a) = (a + 1) (| A-1 | + 2) = (a + 1) 2, monotonically increasing | g (a) ∈ [4,9] when - 32 ≤ a < 1, G (a) = (a + 1) (| A-1 | + 2) = (A-1) 2 + 4, monotonically increasing | g (a) ∈ [- 94,4], the range of G (a) is [- 94,9]

Let f (x) = X2 - (2a + 1) x + 3, if the monotone increasing interval of F (x) is [2, + ∞], then the value of real number a is
Can you tell me how to solve this kind of problem

The opening upward increases to the right of the axis of symmetry
So the axis of symmetry is x = 2
F (x) = x & sup2; - (2a + 1) x + 3 the axis of symmetry is x = - [- (2a + 1)] / 2 = 2
2a+1=4
a=3/2

If the quadratic function f (x) = x2-ax + 2a-1 has zero and is an integer, then the set of values of real number a is:

F (x) = x & # 178; - ax + 2a-1 has zero point, which shows that f (x) = 0 has solution  f (x) = x & # 178; - ax + 2a-1 = 0 △ = A & # 178; - 4 (2a-1) = A & # 178; - 8A + 4 ≥ 0, a ≤ 4-2 √ 3 ≈ 0.54 or a ≥ 4 + 2 √ 3 ≈ 7.5  A is an integer, and the integer that  a cannot take is between 0.54 and 7.5 

Xiao Ming read an 84 page story book. On the first day, he read 14 of the whole book. On the second day, he read 13 of the whole book______ Page, and______ I didn't look at the page. On the third day, I started from the third______ The page looks good

84 × (14 + 13) = 84 × 712 = 49 (page) 84-49 = 35 (page) 49 + 1 = 50 (page) answer: I have read 49 pages in two days, and there are still 35 pages left. On the third day, I will start from page 50

The sum of the two sides of the triangle is 10, and the cosine of the angle is the root of the equation 2x ^ 2-3x-2 = 0

A + B = 10, the angle is C
2x²-3x-2=0
x=2,x=-1/2
-1=5√3
So the minimum perimeter is 10 + 5 √ 3
ab

The distance between the two places is 600 kilometers. The bus can travel one eighth of an hour, and the truck takes 10 hours to complete the whole journey. How many hours will the two cars meet each other?

Method 1
1 ÷ (1 / 8 + 1 / 10) = 40 / 9 hours
Method 2
The bus runs every hour
600 × 1 / 8 = 75 km
The truck runs every hour
600 △ 10 = 60 km
When did you meet
600 ÷ (75 + 60) = 40 / 9 hours

If the quotient of two rational numbers is positive and the sum is negative, then the two numbers

All negative numbers

A total of 200 people go for an outing. 45 people can take a big car and 20 people can take a small car. How can it be cost-effective?
1. The cost of the big car is 300 yuan, and the cost of the small car is 200 yuan. How much does the car rental cost for a day?
2. How much does it save for all teachers and students to buy tickets according to the group ticket price compared with the individual ticket price? (individual ticket price: 2 yuan for one person; group ticket price: 1.5 for one person)

(1) Four big cars and one small car! 4x45 = 180 + small car 20 = 200 people! 4x300 = 1200 yuan + small car 200 = 1400 yuan! The rental fee is 1400 yuan a day!
(2) 200x2 = 400-200x1.5 = 300 = 100 (yuan)

To find the solution of; x minus three fourths, x equals three tenths, is a process

x-3/4x=3/10
1/4x=3/10
x=6/5