The rational number a is not equal to B. the sum of arithmetic square roots of a and B is irrational

The rational number a is not equal to B. the sum of arithmetic square roots of a and B is irrational

Suppose √ a + √ B is a rational number, let it be q, that is √ a + √ B = q, then √ a = q - √ B, the square of both sides, get a = Q & # 178; - 2q √ B + B, because √ B is an irrational number, Q ≠ 0, so - 2q √ B is an irrational number, and Q & # 178; + B is a rational number, so Q & # 178; - 2q √ B + B is an irrational number, and the left side of the equation is

There are three mutually unequal rational numbers, which can be expressed as 1, a + B, A. or 0, B / A, B. what is the sum of the cube root of a minus the arithmetic square root of B

Three unequal rational numbers
A ≠ 0, otherwise a / b = 0 and 0 are contradictory
Only a + B = 0, a = - B, a / b = - 1
b=1,a=-1
The square root of A-B = - 1-1 = - 2

Do you know where mathematical coding is used in computers?

There is no place for computers not to use digital coding. The data processed by computers are composed of "0" and "1"
CPU operation, memory addressing, programming, data transmission and so on, all need to use digital coding

How to solve the factorization of A2 (B + C) - B2 (a + C) - C2 (a + b) + 3ABC,

=a2b+a2c-b2a-b2c-c2a-c2b+3abc
=ab(a-b)+abc+ac(a-c)+abc-bc(b+c)+abc=ab(a-b+c)+ac(a-c+b)-bc(b+c-a)

For a number with an exponent, does the exponent have to be an integer or a decimal?

Let y = 2 ^ x, and then you draw its function curve, take a look at the value range of X, you should know that x can be a decimal!

Can the exponent of a power be a decimal

Yes
For example, 2 ^ 0.5 = √ 2
It can even be any real number, such as irrational number 3 ^ (√ 2). However, due to its complex nature, it is generally not discussed. This paper deals with the theory of transcendental numbers. The study of transcendental numbers began in Liouville
There is a conclusion for reference
Gerfond Schneider theorem: if a is any algebraic number other than zero and one and B is an irrational algebraic number, then a ^ B must be a transcendental number

The index of - 1.032 × 10 ^ - 5 is - 5 in scientific counting method. How many decimal places can you judge this number?

8

If the integer of [(√ 17) + 4)] 2n + 1 is a and the decimal is B. It is proved that B (a + b) = 1, where 2n + 1 is the exponent

∵(√17+4)^(2n+1)-(√17-4)^(2n+1)
=C(1,2n+1)17^n*4+C(3,2n+1)17^(n-1)4^3+C(5,2n+1)17^(n-2)4^5+...+C(2n+1,2n+1)4^(2n+1)
This number is a positive integer
∵0

If the exponent is a decimal?
Can the exponent be a decimal?
It's like: 0.5
The 0.5th power of 4
Is this ok?
If the exponent is a decimal, how to calculate it?

44 ^ 0.5 = 44 ^ 1 / 2 = 44 under root

Understanding of factorization
1. (2004 * Fuzhou) factorization factor A ^ 2-25 = 2. (2004 * Changsha) factorization factor XY ^ 2-x ^ 2Y = 3. (2004 * Guiyang) factorization factor X ^ 2-1 = 4. (2004 * Nanjing) factorization factor 3x ^ 3-3 = 5. (2004 * Hubei) factorization factor X ^ 2 + 2XY + y ^ 2-4 = 6. (2004 * Shaanxi) factorization factor X ^ Y3 ^ 2-4x = 7. (2004 * Guangzhou) factorization factor 2x ^ 2-2 = 8. (2004 * Guilin) factorization factor A ^ 3 + 2A ^ 2 + A= 9. (2004 * Qinghai) decomposition factor X ^ 2y-4xy + 4Y = 10. (2004 * Harbin) decomposition factor A ^ 2-2ab + B ^ 2-C ^ 2=

1. A-25 = a-5 = (a + 5) (a-5), [square difference formula] 2, XY xy = XY (Y-X), [extract common factor] 3, X-1 = X-1 = (x + 1) (x-1), [square difference formula] 4, 3x-3 = 3 (x-1) = 3 (x-1) (x + X + 1), [cubic difference formula] 5, x + 2XY + y-4 = (x + y) - 2 = (x + y + 2) (x + Y-2), [complete