On the calculation of real numbers √ 2004 * 2005 * 2006 * 2007 + 1 [i.e. add a root outside (the whole root, twice root)] should have a detailed process,

On the calculation of real numbers √ 2004 * 2005 * 2006 * 2007 + 1 [i.e. add a root outside (the whole root, twice root)] should have a detailed process,

First, let's look at the general formula. √ n (n + 1) (n + 2) (n + 3) + 1
∵n（n+3）=n²+3n
（n+1）（n+2）=n²+3n+2
√ n (n + 1) (n + 2) (n + 3) + 1 = √ (n & sup2; + 3n) (n & sup2; + 3N + 2) + 1 [take n & sup2; + 3N as a whole] = √ (n & sup2; + 3n) & sup2; + 2 (n & sup2; + 3n) + 1 = √ (n & sup2; + 3N + 1) & sup2; = n & sup2; + 3N + 1
Back to this topic. √ 2004 * 2005 * 2006 * 2007 + 1 = 2004 & sup2; + 3 × 2004 + 1 = 4022029

Given the arithmetic square root of 3x-y + | Y-9 | = 0, try to judge whether the x square root of Y is rational or irrational?

Because the arithmetic square root of 3x-y + | Y-9 | = 0
So 3x-y = 0, Y-9 = 0
So x = 3, y = 9
So the root of X of y = the root of 3 times, 9, is an irrational number

When x = 36, enter x, take the arithmetic square root, is it irrational or rational, and then output y

Rational number

After the letter A2 + 5ab + 6b2 + A + 3b is the exponent, factorization

Factorization letter formula to complete, thank you
See the formula clearly

(a+b)²=a²+2ab+b²
(a-b)²=a²-2ab+b²
a²-b²=(a+b)(a-b)
(a+b)³=a³+3a²b+3ab²+b²
(a-b)³=a³-3a²b+3ab²-b³
a³+b³=(a+b)(a²-ab+b²)
a³-b³=(a-b)(a²+ab+b²)

X2-6xy + 9y2-4x + 12Y is followed by the exponential factorization

x2-6xy+9y2-4x+12y
=(x²-6xy+9y²)-(4x-12y )
=(X-3Y)²-4（x-3y）
=(X-3Y)(X-3Y-4)

What are the times and exponents of a natural number?
For example: 2
If the number of times is 0, that is to say, 2 × (any letter) and the index of the letter is 0, 0 × (any letter), doesn't it get 0?
But if you multiply them, you'll get 0

The degree of a natural number is 0
The index is the number of times, also 0
The coefficient is himself

Can the exponent of a number be negative

Yes, 2 ^ (- 1) = 1 / 2

If the exponent of a number is negative, what is the number

In high school mathematics, if you want a number with negative exponent, that is, a ^ n = B, you need to satisfy a

How to solve the unary unknowns with exponent
3597.42=2500x+1000x^0.5
Help to see how to find x

Let x = y ^ 2 (Y ≥ 0) have
3597.42=2500y^2+1000y
If you square y, you will find the solution of X