Decomposition factor: the second power of 4 (a + b) + 16 (a + b) + 16

Decomposition factor: the second power of 4 (a + b) + 16 (a + b) + 16

4(a+b)^2+16(a+b)+16
=4[(a+b)^2+4(a+b)+4]
=4(a+b+2)^2
The second power of 4 (a + b) + 16 (a + b) + 16
=[2(a+b)]²+16(a+b)+4²
=[2a+2b+4]²
The second power of X (y) - the third power of 4 (x)
xy²－4x³
=x(y²－4x²)
=x(y＋2x)(y－2x)
xy²-4x³
=x(y²-4x²)
=x(y+2x)(y-2x)
xy2 -4x3
=x(y2-4x2)
=x(y-2x)(y+2x)
(x + y) ((x + y) 2 times power - 6 (x + y) + 1]
=(x + y) (x + y) - 1]
= （X + Y）（3X +3 Y +1）（3 +3 Y-1）
The quadratic equation of one variable x ^ 2 -- (R-R) x + 1 / 4D ^ 2 has no real root
R is the radius of circle O1, R is the radius of circle O2, D is the center distance
Is x ^ 2 -- (R + R) x + 1 / 4D ^ 2 = 0
The discriminant △ = B & sup2; - 4ac, △ > b & sup2; - 4ac, △
There is no real root, so (R-R) ^ 2-D ^ 2
Solving inequality - x + 7 > 7x-3
Give reasons
-x+7＞7x-3
-x-7x＞-7-3
-8x＞-10
X
Item transfer: - x-7x > - 3-7
－8x>-10
Divide both sides by - 8 at the same time, and the direction of inequality should be changed
x-10
4x
In the triangle ABC, if Tana and tanb are the two roots of the equation 6x ^ 2-5x + 1 = 0, find the angle C
If C = 90 °, find the maximum of sina * SINB
(1) Solve the equation X1 = 1 / 2, X2 = 1 / 3, Tan (a) + Tan (b) = 5 / 6, Tan (a) * Tan (b) = 1 / 6
(2)tan(A+B)=[TAN(A)+TAN(B)]/[1-(TAN(A)*TAN(B)]
=1
(3)A+B=45°
（4）C=135°
C=90°,SINA*SINB=SINA*COSA=1/2*SIN(2A)
90°＞A＞0,180°＞2A＞0
When 2A = 90 °, the maximum value of sina * SINB is 1 / 2
It can be concluded that Tana and tanb are 1 / 2 and 1 / 3 respectively
=The formula Tan (a + b) = (Tan a + Tan b) / (1-tan a * Tan b) is used to obtain Tan (a + b) = 1, that is, a + B = 45 ° and the angle c is 135 °
Given that the solution set of inequality system 3a − 2x ＞ x2 − 3x − 22 ＞ B − 1 is 1 ＜ x ＜ 2, find the value of a + B
3A − 2x ＞ 12x − 3 (1) x − 22 ＞ B − 1 (2), solution (1) is x ＜ 6A + 65, solution (2) is x ＞ 2B, the solution set of ∵ inequality system is 1 ＜ x ＜ 2, ∵ 6A + 65 = 22b = 1, solution (1) is a = 23B = 12, ∵ a + B = 23 + 12 = 76
5x-2y=-8；7x-6y=-40
Equations, and the addition and subtraction elimination method
solution
5x-2y=-8 (1)
7x-6y=-40 (2)
(1) Three times
15x-6y=-24 (3)
(3) - (2) get
8x=16
∴x=2
∴y=9
5x-2y=-8①；7x-6y=-40②
1 times 3 minus 2,
8x=16,x=2
So y = 9
It is known that the solution set of 3a-2x > 1 / 2x-3 (X-2) / 2 > B-1 is 1
3a-2x＞1/2x-3
-5/2x＞-3a-3
x＜6/5（a+1）
Similarly: (X-2) / 2 > B-1
It can be concluded that x ＞ 2B
∴2b＜x＜6/5（a+1）
∵1＜x＜2
So 2B = 1
6/5（a+1）=2
The solution is a = 2 / 3, B = 1 / 2
So a + B = 2 / 3 + 1 / 2 = 7 / 6
2x-y = 105x + 6y = 42 to solve the equations
2x-y=10*6
12x-6y = 60 (1)
5x+6y=42（2）
（1）+（2）17x=102
X=6
Substituting the value of X into
Y=2
Then x = 6, y = 2
2x-y=10*6
12x-6y = 60 (1)
5x+6y=42（2）
（1）+（2）17x=102
X=6
Substituting the value of X into
Y=2
If the solution set of the inequality system {2x-a ＜ 2B x-3a ＞ B is 2 ＜ x ＜ 5, the value of a can be obtained
2x-a3a+b
3a+b