(chapter on the complete square formula) What is the relationship between a and B when the algebraic formula 4-a-b + 2Ab reaches the maximum value?

It can be reduced to 4 - (a-b), so when a = B, the maximum value is 4

Help to solve three math problems, seventh grade complete square formula and so on [2A ^ 2 (3AB ^ 2) ^ 3 × 1b of 2 - (- 3AB) ^ 2 A ^ 2] / (- 3A ^ 2b) ^ 2 (x-2)^2(x+2)^2-(1+2x)^2(2x-1)^2 40.8×29.2+0.8^2

40.8×39.2+0.8^2

Seventh grade mathematics problem -- factorization of complete square formula 1 * 2 * 3 * 4 + 1 = -- = (---) square 2 * 3 * 4 * 5 + 1 = --- = (---) square 3 * 4 * 5 * 6 + 1 = --- = (---) square Guess a (a + 1) (a + 2) (a + 3) + 1 = (--------) square and explain your reasons

1x2x3x4+1=25=5²2x3x4x5+1=121=11²3x4x5x6+1=361=19²a(a+1)(a+2)(a+3)+1=(a²+3a)(a²+3a+2)+1=(a²+3a)²+2(a²+3a)+1=(a²+3a+1)²

Mathematical problems of complete square formula Given that a + B = 3, ab = - 12, calculate the following values: （1）a²＋b²；（2）（a-b）²

a²＋b²=(a＋b)^2-2ab=9-2*(-12)=33
(a-b）²=a²＋b²-2ab=33-2*(-12)=57

If the system of equations about X and Y ax+3y＝9 If 2x − y = 1 has no solution, then a = () A. -2 B. -6 C. 0 D. 2

Original equations
ax+3y＝9①
2x−y＝1② ，
Y = 2x-1 is obtained from ②,
Substituting ①, ax + 6x-3 = 9,
X = 12
a+6，
If a + 6 = 0, then a = - 6
Therefore, B

It is known that the solution of {X-Y = 3A, 2x-3y = A-1 is also the solution of X + y = 5

{X-Y=3a,（1）
2X-3Y=a-1（2）
(1) × 2 - (2)
Y=5a+1；
In (1), we get the following results:
x=8a+1;
x+y=8a+1+5a+1=13a+2=5;
13a=3;
a=3/13;
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2x-3y = 1 and X + 3Y = 5
The solution x = 2 is replaced by y = 1 in the above formula
Then replace x = 2, y = 1 into ax + 2Y = 7
A = 2.5

Why the factorization Δ of 6x ^ 2-xy-2y ^ 2 + ay-6 must be a complete square formula and Δ of Δ must be 0

∵ 6x ∵ 2 - xy-2y ∵ y-6 can decompose factors in the range of rational numbers
The discriminant of the quadratic equation of X: 6x? - xy-2y? + ay-6 = 0
Δ = y? + 48y? - 24ay + 144 = 49y? - 24ay + 144 must be a complete square (otherwise, the root sign cannot be decomposed into rational factors)
It is transformed into the equation about y: 49y? - 24ay + 144 = 0 has two equal real roots
Then the discriminant Δ of the root of the equation must be 0
That is (24a) 2 - 4 × 49 × 144 = 0
A = ± 7 is obtained

Factorization factor (x ^ 2 + y ^ 2-z ^ 2) ^ 2-4x ^ 2Y ^ 2

The square difference formula (x ^ 2 + y ^ 2-z ^ 2) is ^ 2-4x ^ 2 ^ 2 ^ 2 ^ 2-4x ^ 2 ^ 2 ^ 2-4x ^ 2 ^ 2 ^ 2-4x ^ 2 ^ 2 ^ 2-4x ^ 2 ^ 2 ^ 2-4x ^ 2 ^ 2-4x ^ 2 ^ 2-4x ^ 2 ^ 2-4x ^ 2 ^ 2 ^ 2-4x ^ 2 ^ 2-4x ^ 2-z ^ 2 ^ 2-4x ^ 2-z ^ 2 ^ 2-4x ^ 2 ^ 2-4x ^ 2 ^ 2 ^ 2-4x ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2-4x ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ 2 ^ + Z) (x + Y-Z) (X-Y + Z) (X-Y-Z)

(1) If x ^ 2-mx + 16 is a complete square formula, then M = (2) factorization factor: 2x ^ 3-4x ^ 2Y + 2XY^

(1) If x ^ 2-mx + 16 is a complete square formula, then M = 8
(2) Factorization factor: 2x ^ 3-4x ^ 2Y + 2XY^
=2x(x^2-2xy+y^2)
=2x(x-y)^2

(chapter on the complete square formula) What is the relationship between a and B when the algebraic formula 4-a-b + 2Ab reaches the maximum value?