Given that integer a satisfies 4-A > 0 and 4a-3 > 0, what is the solution of the quadratic equation x (ax-3) = 2 + X?

4a-3>0,a>3/4
4-a>0,a

If x = 5 is the solution of the equation AX + 5 = 10-4a, then a=______ ．

Substituting x = 5 into the equation, we get 5A + 5 = 10-4a, and the solution is a = 59

The minimum integer solution of 3 (x + 5) is the solution of equation 2x AX = 4, and the value of 4a-a / 4 is obtained

2-2x0 x>-13/5
The minimum integer solution is x = - 2
-4+2a=4 a=4 4a-a/4=16-1=15

A is a real number, and the quadratic equation 7x ^ 2 (a + 13) x + 2A + 2 = 0 of X has two real number roots, which are between 0 and 1 and 1 and 2 respectively

Analysis: for quadratic function, if there is a root between two numbers, the corresponding function value is different sign or the product is negative
Explanation: the meaning of the question is very clear
(2a+2)(7+a+13+2a+2)

If a two digit number cannot be divided by (?), then the two digit number must be prime

A two digit number is a prime number. A two digit number is composed of two numbers, two digits
My mother bought some oranges. Xiao Ming ate more than half of them on the first day, less than two on the second day, and five more. How many oranges did my mother buy?

If mother bought x oranges, then as follows
The first day: X / 2 + 2
The next day I ate: [x - (x / 2 + 2)] / 2 - 2
The total number of oranges is x = x / 2 + 2 plus [x - (x / 2 + 2)] / 2 - 2 plus 5
So x = 16

19 multiplied by one product is prime; multiplied by another product is composite and can be 1, 2, 3, 4 What are the two numbers (not fractions or decimals)?

Because 19 times a number product is prime, this number can only be 1; times another number product is composite, and can be 1, 2, 3, 4 Natural number can be divided by 1, 2, 3 and 4. This number is 12, so the two numbers (not fractions or decimals) are 1 and 12 respectively. Answer: the two numbers (not fractions or decimals) are 1 and 12 respectively

To determine whether n is a prime, we only need to divide it by the integer between 2 and root n?
RT, to determine whether n is a prime, it only needs to be divided by the integer between 2 and the root n. if it can't be divided, it is a prime?
Why root n?
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If a number n is a composite number, it can be written as n = P * Q * The more items, the smaller the quality factor
Let p be the minimum prime factor of N, then 2 = P
That is, n = PQ > = P * P > sqrt (n) * sqrt (n) = n, which is contradictory, so the hypothesis is not true, that is, P

It is proved that there are innumerable positive integers a with the following properties. For any positive integer n, n ^ 4 + A is not prime

If n is odd
N ^ 4 is odd
A as long as it is odd (greater than 1)
that
Odd + odd = even
N ^ 4 + A is not a prime number. There are innumerable a's;
If n is even
N ^ 4 is even
A as long as it is even (greater than 0)
that
Even + even = even
N ^ 4 + A is not a prime number. There are innumerable a's
therefore
Set up

Let C not be divisible by the square of prime, if A2 | B2C, then a | B

In order to prove a|b, we only need to prove: for any prime P, suppose that the degree of P in the prime decomposition of a is s, and the degree of P in the prime decomposition of B is t, then t > = s
To the contrary: hypothesis t

Given that integer a satisfies 4-A > 0 and 4a-3 > 0, what is the solution of the quadratic equation x (ax-3) = 2 + X?