Given that the sum of two prime numbers is 21, then the product of the two prime numbers is______ ．

Because the sum of two prime numbers is odd, one prime number must be odd and the other even. Because 2 is the only even prime number, the other prime number is 19, so their product is 2 × 19 = 38

We are two prime numbers. Our sum is 10 and our product is 21. What are we?

Decompose 21 into prime factor: 21 = 3 × 7, so the two prime numbers are 3 and 7

How to find the monotone increasing interval and monotone decreasing interval of logarithmic function (compound)?

It's most convenient to find the derivative directly. If you don't know the derivative, you can look out from the innermost layer in turn. When increasing function, the monotonicity will not change, but when decreasing function, the monotonicity will change

Is there () in absolute value sign

There can be some combination calculation in the absolute value symbol. In this way, there can be brackets. If it is the final result, there is no need to add brackets

F (x) = LG [(2 / 1-x) + a] is an odd function?
Now we only use f (2) = - f (- 2) according to the definition to calculate that a has two values - 1 or 7 / 3. Which one do you want, and why
Solving without f (0) = 0

If x ≠ 1 is known, then x ≠ - 1. If the original assumption holds, then when x = - 1 is, that is [2 / (1 + 1) + a] ≤ 0, the solution is a ≤ - 1

It is known that the function f (x) = ax + B1 + X2 is an odd function defined on (- 1,1), and f (12) = 25. (1) try to find the analytic expression of the function f (x); (2) prove that the function is monotone increasing in the domain of definition

(1) ∵ function f (x) = ax + B1 + X2 is an odd function defined on (- 1,1), and ∵ f (0) = 0, that is, B = 0, f (12) = 25, ∵ A21 + 14 = 25, the solution is a = 1 ∵ f (x) = X1 + x2. (2) take any two numbers x1, X2 ∈ (- 1,1), and X1 < X2, then f (x1) - f (x2) = X11 + x12-x21 + X22 = (x1 − x2) (1 − x1 · x2) (1 + X12) (1 + X22) < 0, because x1, X2 ∈ (- 1,1), and X1 < X2, Therefore, the function f (x) = ax + B1 + x2 increases monotonically on (- 1,1)

Why is the result of the set of function values of quadratic function y = x & # - 4 greater than or equal to negative four

Because x ^ 2 ≥ 0
So x ^ 2-4 ≥ - 4
That is y ≥ - 4
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A mathematical problem of rational number subtraction
The highest price of a stock on the first day is 0.3 yuan higher than the opening price, and the lowest price is 0.2 yuan lower than the opening price; the highest price on the second day is 0.2 yuan higher than the opening price, and the lowest price is 0.1 yuan lower than the opening price; the highest price on the third day is equal to the opening price, and the lowest price is 0.13 yuan lower than the opening price

High is + and low is -
First day + 0.3 - (- 0.2) = 0.5
On the second day, + 0.2 - (- 0.1) = 0.3
The third day: 0 - (- 0.13) = 0.13
Average (0.5 + 0.3 + 0.13) / 3 = 0.31

The position of the corresponding point of rational number A.B on the number axis is shown in the figure, then the following size relation is correct: A.A is greater than - B.A is greater than B.C. - A is greater than B.D. - B is greater than a
A means - 1.5
B means 2.5

a>-b,b>-a
A

To solve the equation of X: ax + B - (3x + 2Ab) / 3 = 1 / 2

By multiplying both sides of the original equation by 6, we get that 6AX + 6b-6x-4ab = 3, 6 (A-1) x = 3 + 4ab-6b
1、 When a = 1, the original equation can be changed to 0 = 3 + 4b-6b = 3-2b
Obviously, when B = 3 / 2, the solution of the equation is all real numbers, otherwise there is no solution
2、 When a ≠ 1, the solution of the equation is x = (3 + 4ab-6b) / (6a-6)
To sum up, the solutions of the original equation are different due to the different values of a and B
1. When a = 1 and B = 3 / 2, there are infinitely many solutions, then x = all real numbers
2. When a = 1 and B ≠ 3 / 2, there is no solution
3. When a ≠ 1, the solution of the equation is: x = (3 + 4ab-6b) / (6a-6)

Given that the sum of two prime numbers is 21, then the product of the two prime numbers is______ ．