Given that the solution of equation AX plus I2 equals 0 is x equals 3, then the solution set of inequality (a + 2) x < - 6 is

Given that the solution of equation AX plus I2 equals 0 is x equals 3, then the solution set of inequality (a + 2) x < - 6 is

X = 3 is substituted into the equation
3a+12=0
a=-4
Substitution inequality
-2x3

Given that x = 5 is the solution of the equation AX-8 = 20 + A, then the value of a is ()
A. 5B. 6C. 7D. 143

Substituting x = 5 into the equation: 5a-8 = 20 + A, the solution: a = 7

It is known that x equals 5 is the solution of the equation AX minus 16 equals 12 plus a. the solution of the equation is used to find the value of A

5a-16=12+a
5a-a=12+16
4a=28
a=7

In proving that root 2 is irrational, why is PQ prime?

It is not said that PQ is a prime number, but P and Q are coprime numbers. Coprime does not mean that they are all prime numbers, but means that the greatest common divisor of P and Q is 1

It is proved that P / Q + radical 2 is irrational

Because there are no restrictions on P and Q,
So whether P / Q + √ 2 is rational or irrational is uncertain
Therefore, it is impossible to talk about the problem of "proving that P / Q + radical 2 is irrational"
If we want to make this proposition true, we must change it to
If P and Q are integers and Q ≠ 0, it is proved that P / Q + √ 2 is an irrational number
for example
When p = 1, q = 2, P / Q + √ 2 = 1 / 2 + √ 2 is irrational
When p = 1, q = 1 - √ 2, P / Q + √ 2 = 1 / (1 - √ 2) + √ 2 = - (1 + √ 2) + √ 2 = - 1 is a rational number

Does irrational number have square root?

A positive irrational number has two square roots, which are opposite to each other
Negative irrational numbers have no square root

How to find the square root of irrational number

Irrational numbers are infinite non cyclic decimals, and the number of digits is naturally endless. However, we always need to have a certain accuracy in our calculation, which requires that we can find the finite digits. Therefore, we can express them as decimals of a certain number of digits, and then do open operation
(a+b)^2=a^2+2ab+b^2=a^2+(2a+b)*b
b=[(a+b)^2-a^2]/(2a+b)
Generally in junior high school, just do it

The open root sign of prime product is irrational
If P1, P2 , Pt is a prime number, then P1, P2, P3 , Pt is irrational!

Let √ p be a rational number, then √ P can be written as a fraction. Let √ P = m / N, where m and N are coprime positive integers, then: P = m ^ 2 / N ^ 2, that is, p * n ^ 2 = m ^ 2. From the above formula, we can see that m ^ 2 has a divisor P, that is, M has a divisor P, that is, let m = PK, where k is a positive integer, then: P * n ^ 2 = m ^ 2 = (PK) ^ 2 = P ^ 2 * k ^ 2, that is, n ^ 2 = P * k ^ 2 from above

All prime numbers are not divisible by two______ ．

2 is a prime number, 2 △ 2 = 1; 2 can be divided by 2

What number is not divisible by the square of any prime number

Such numbers are called square free numbers and generally exclude 1 (and - 1)
Including all prime numbers and all any number of prime number product (and its opposite number)
in my submission,
The distribution of this kind of numbers is closely related to the distribution of prime numbers