If real numbers a and B satisfy real numbers a and B satisfy a & sup3; + B & sup3; + 3AB = 1, find the value of a + B The third power of a)

If real numbers a and B satisfy real numbers a and B satisfy a & sup3; + B & sup3; + 3AB = 1, find the value of a + B The third power of a)

From the meaning of the question: (a + b) (a ^ 2 + B ^ 2-AB) + 3AB = 1
（a+b）[（a+b）^2-3ab]+3ab=1
（a+b）（a+b）^2-3ab（a+b）+3ab-1=0
[（a+b）^3-1]-3ab（a+b-1）=0
（a+b-1）[（a+b）^2+1+a+b]-3ab（a+b-1）=0
（a+b-1）[（a+b）^2+1+a+b-3ab]=0
(a + B-1) = 0 or (a + b) ^ 2 + 1 + A + b-3ab = 0,
From (a + b) ^ 2-3ab + (a + b) + 1 = 0, a ^ 2 - (B-1) a + (b ^ 2 + B + 1) = 0,
And ∵ a, B are real numbers, so the above equation has real number solutions,
△=（b-1）^2-4（b^2+b+1）≥0
That is: (B + 1) ^ 2 ≤ 0,
So: B = - 1, substituting in the above formula, a = - 1,
So a + B = - 2;
To sum up, a + B = 1 or a + B = - 2

The size of the cubic power of X compared with the square of x-x + 1
When x is greater than 1, I get the result
x〔x（x－1）－1 〕＋1
But now it's less

x> X ^ 3 - (x ^ 2-x + 1) = (x ^ 2 + 1) (x-1) > 0. This expression merges one or three terms, two or four terms, and finally merges two new terms. It's OK. It seems that the formula you solved can't be used for comparison, isn't it a difference method?

It is known that a and B belong to positive real numbers, and a is not equal to B. This paper proves: (a + b) square (a square - AB + b square) > (a square + b square) square

-Square of B + 3AB + (- 4AB) =?

(-b)²+3ab+(-4ab)
=b²-ab
=b(b-a)

The square of 3AB + B+____ =What should be filled in the horizontal line for the square of 4ab-b?

3ab+b²+__ ab-2b²__ =4ab-b²

If a's Square - AB = 3, 4ab-3b's Square = - 2, then what is the value of a's square + 3ab-3b's Square

From the known conditions a & # 178; - AB = 3 and 4ab-3b & # 178; = - 2
Add the above two equations:
That is: A & # 178; + 3ab-3b & # 178; = 3-2 = 1

What is composite number and composite number sequence?

1. Compound number: a mathematical term used to refer to the number that can be divided by other numbers in addition to 1 and the original number
2. In addition to 1, some numbers can not be divided by other integers except 1 and itself, such as 2, 3, 5, 7, 11, 13, 17,..., which are called prime numbers. Some numbers can be divided by other integers except 1 and itself, which are called composite numbers, such as 4, 6, 8, 9, 10, 12, 14,..., which are composite numbers, In this way, all natural numbers can be divided into three categories: 1, prime and composite. Composite sequence - term explanation, such as 4, 6, 8, 9, 10, 12, 14,... Is called composite sequence

What is a composite sequence? 4,6,8,9,10,12. And 4,6,8,10,12. Which is a composite sequence? Or is the first one?

4,6,8,9,10,12.

Please explain the basic principle and formula of decomposition prime factor, which represents a composite number with () and is called decomposition prime factor

To express a composite number in the form of multiplication of several prime numbers is called decomposition prime factor
For example: 24 = 2 × 2 × 2 × 3

The minimum sum with a factor of 7 is () and the maximum two digit sum is ()

The minimum sum with a factor of 7 is (14), and the maximum two digit sum is (98)