If the negative reciprocal of a is 8 and the negative reciprocal of B is 8, then (a) A. a=bB. a＜bC. a＞bD. ab=1

From the inverse of the negative reciprocal of a is 8, we can get: - - 1A = 8, we can get a = 18. From the inverse of B, we can get: - (1 − b) = 8, we can get b = 18. Therefore, a = B

Why is the sentence "if the reciprocal of a real number is itself, then the number must be 1" wrong?

（-1）*（-1）=1
So besides 1, the reciprocal of - 1 is itself

The reciprocal forms a set of its own real numbers, right

Wrong. The reciprocal of 1 is 1. The set can't have duplicate elements. I think it's wrong

The equation x & sup2; + X + M = 0 (M belongs to R) has two imaginary roots x (1), X (2), and | x (1) - x (2) | = 3, so we can find the value of M

|X (1) - x (2) | = less than 3 square
(x1-x2)^2=9
x1^2-2x1x2+x2^2=9
x1^2+2x1x2+x2^2-4x1x2=9
(x1+x2)^2-4x1x2=9
(-1)^2-4m=9
4m=1-9=-8
m=-2

It is known that the set a = {a x + A + X & # 178; - 2 = 1} has a unique real number solution, and the set a is represented by enumeration

x²-2=x+a
X & # 178; - x-a-2 = 0 has unique real solution
△=4a+9=0
a=-9/4
Set a = {- 9 / 4}

1. It is known that the set a = {a (x + a) / (X & # 178; - 2) = 1) has a unique real number solution}?
2. It is known that the solution set of inequality (AX-5) / (X & # 178; - a) < 0 about X is m. if 3 ∈ m, and 5 & # 8713; m, find the value range of real number a?
Question: 1, 2, in the question, is the denominator ≠ 0, because the answer does not consider that the denominator is not zero

1. The set a = {a (x + a) / (X & # 178; - 2) = 1) has a unique real number solution} obviously, x + a = x ^ 2-2 has a unique real number solution, or there are two solutions, but there is one such that the denominator is 0I) has a unique real number solution, then Δ = 1 + 4 (a + 2) = 9 + 4A = 0, that is, a = - 9 / 4ii) has two solutions, but there is one such that the denominator is 0, let x ^ 2-2 = 0 get x = ± √ 2, then

Given that the set a = {a | (x-a) (x-a & # 178; + a) / X-2 = 0 has a unique real number solution}, the enumeration method is used to represent the set a

1. A = a ^ 2-A ≠ 2, the solution is a = 0;
2. If a = 2 and a ^ 2-A ≠ 2, or a ^ 2-A = 2 and a ≠ 2, the solution is a = - 1,
So a = {0, - 1}

What is the concept of "imaginary number"?
It's more popular

This is the concept of complex number a + bi copied from the mathematics book of grade 3. When B is not equal to 0, it is called imaginary number ~ a = 0, when B is not equal to 0, it is called pure imaginary number ~ A, and B is called real part and imaginary part ~ imaginary number respectively. The unit of imaginary number I was first introduced by Euler. He took the prefix of imaginary (imaginary, imaginary) as the imaginary unit, I = √ - 1

The concept and definition of imaginary number

This is a copy from a math book in grade three~
In complex number a + bi, ~ when B is not equal to 0 ~ is called imaginary number ~ a = 0, when B is not equal to 0 ~ is called pure imaginary number~
A. B is called real part and imaginary part respectively~
The concept of imaginary number
The unit of imaginary number I was first introduced by Euler. He took the prefix of imaginary (imaginary, imaginary) as the unit of imaginary number, I = √ - 1, so all imaginary numbers have the form of Bi. But the determination of imaginary numbers owes to two amateur mathematicians in the 18th century, one is wessel, a Norwegian surveyor, and the other is aergan, an accountant in Paris
We know that real numbers correspond to imaginary numbers, including rational numbers and irrational numbers, that is to say, they are real numbers
Rational number appeared very early, it is accompanied by people's production practice
The discovery of irrational numbers should be attributed to the Pythagorean School in ancient Greece. The emergence of irrational numbers contradicts Democritus' atomism. According to this theory, the ratio of any two line segments is nothing more than the number of atoms contained in them. However, Pythagorean theorem shows that there are incommensurable line segments
The existence of incommensurable line segments made the ancient Greek mathematicians feel in a dilemma, because they only had the concepts of integer and fraction in their theory, and they could not fully express the ratio of the diagonal of a square to the side length, that is to say, in their theory, the ratio of the diagonal of a square to the continuous length could not be expressed by any "number", But let it slip away, even to the greatest Greek algebra scientist Diophantine, the irrational solution of the equation is still called "impossible"
The determination of irrational numbers is closely related to the square root operation. For those incomplete square numbers, it is found that their square roots can be found to be infinite acyclic decimals of any number of places without restriction ,E=2.71828182… It is called irrational number
However, when the position of irrational numbers is determined, it is found that even if all rational numbers and nonexistent numbers are used, the problem of solving algebraic equations can not be solved. The simplest quadratic equation such as x 2 + 1 = 0 has no solution in the same range. In the 12th century, the Indian mathematician boshikaro thought that this equation had no solution. He thought that the square of positive number was positive, The square of a negative number is also a positive number, so the square root of a positive number is twofold; a positive number and a negative number, negative number has no square root, so negative number is not a square number. This is equal to not admitting the existence of negative root of equation
In the 16th century, Cardano boldly used the concept of negative square root for the first time in his great Yan Shu. If we don't use negative square root, we can solve the problem of solving quartic equation. Although he wrote the square root of negative number, he hesitated for many times. He had to declare that this expression was fictitious and imaginary, and it was not called "imaginary number" once, Even Euler, a famous mathematician, had to add a comment to his paper when he used imaginary numbers. All the mathematical formulas in the form of √ - 1 and √ - 2 are impossible and imaginary numbers, because they represent the square root of negative numbers. For such numbers, we can only assert that they are neither nothing nor more than nothing, Even less than nothing. They are linear and illusory. Although the master's passage is a bit awkward to read, it can be seen that he and imaginary number are not so straightforward
However, the appearance of imaginary numbers helps irrational numbers a lot. Compared with rational numbers, irrational numbers are not strong enough. But in front of imaginary numbers, they are both real numbers, just like rational numbers. So mathematicians call them real numbers together with rational numbers, which can be distinguished from imaginary numbers, It is not only inseparable from real number, but also often combined with real number to form plural number
Imaginary numbers are called "ghosts of real numbers". In 1637, Descartes called them "imaginary numbers", so all imaginary numbers have Bi, while complex numbers have a = Bi, where a and B are both real numbers. Imaginary numbers are also called pure imaginary numbers
From the beginning of Cardano's Da Yan Shu, in 200 years, the imaginary number has been covered with a layer of mysterious and inconceivable veil. In 1797, wessel gave the image representation of dotted line, and then established the reasonable position of the imaginary number, Later, Gauss established a one-to-one correspondence between the point on the rectangular coordinate plane and the complex number, and the imaginary number was widely known

Does imaginary number have any practical significance?

You don't need it now. In my opinion, it's mainly to study some problems when there is no real number solution. The imaginary number as a solution can explain many problems. When we study the wave function, we often say that the phase difference, or that the wave is composed of simple waves in two directions. At this time, we can introduce the imaginary number, because 1 and I do not interfere with each other

If the negative reciprocal of a is 8 and the negative reciprocal of B is 8, then (a) A. a=bB. a＜bC. a＞bD. ab=1