Solve equation (1) 4x & # 178; = 9 （2）2（x+1）²-4=0 （3）x²-4x+1=0 （4）2x²+2x=1 （5）x²-x-6=0

Solve equation (1) 4x & # 178; = 9 （2）2（x+1）²-4=0 （3）x²-4x+1=0 （4）2x²+2x=1 （5）x²-x-6=0

（1）4x²=9
2x=3 2x=-3
∴x=3/2 x=-3/2
（2）2（x+1）²-4=0
(x+1)²=2
∴x+1=√2 x+1=-√2
∴x=-1+√2 x=-1-√2
（3）x²-4x+1=0
x²-4x+4=3
(x-2)²=3
x-2=√3 x-2=-√3
x=2+√3 x=2-√3
（4）2x²+2x=1
x²+x=1/2
x²+x+1/4=3/4
(x+1/2)²=3/4
x=-1/2+√3/2 x=-1/2-√3/2
（5）x²-x-6=0
(x-3)(x+2)=0
∴x=3 x=-2
(1) Solution x2 = 9 / 4, x = 3 / 2 or - 3 / 2
(2) Solution (x + 1) 2 = 2 x + 1 = positive and negative root sign 2 x = positive and negative root sign 2-1
(3) Solution (X-2) 2 = 3 X-2 = positive and negative root sign 3 x = positive and negative root sign 3 + 2
(4) Solution (x + 1 / 2) 2 = 3 / 4 x + 1 / 2 = positive and negative root sign 3 / 4 x = positive and negative root sign 3 / 4-1 / 2
(5) Solution (x-3) (x + 2) = 0, x = 3 or x = - 2
1)4x²=9
x²=9/4
x1=3/2,x2=-3/2
2)x²-4x+1=0
x²-4x+4=3
(x-2)²=3
X-2 = √ 3 or X-2 = - √ 3
x1=√3+2,x2=-√3+2
3)2x²+2x=1
x²+x=1/2
X & # 178; + X + 1 /... Expansion
1)4x²=9
x²=9/4
x1=3/2,x2=-3/2
2)x²-4x+1=0
x²-4x+4=3
(x-2)²=3
X-2 = √ 3 or X-2 = - √ 3
x1=√3+2,x2=-√3+2
3)2x²+2x=1
x²+x=1/2
x²+x+1/4=3/4
(x+1/2)²=3/4
X + 1 / 2 = 1 / 2 √ 3 or x + 1 / 2 = - 1 / 2 √ 3
X1 = (√ 3-1) / 2 or x2 = (- √ 3-1) / 2
4)x²-x-6=0
(x-3)(x+2)=0
X1 = 3, X2 = - 2, put away
Solution equation: 25 / 16 (1-4x) &# 178; = 1
Hello: 25 out of 16 (1-4x) & # - 178; = 1 (4x-1) & # - 178; = 16 / 254x-1 = ± 4 / 5 4x = 4 / 5 + 14x = 9 / 5x = 9 / 20 or 4x = - 4 / 5 + 14x = - 1 / 5x = - 1 / 20 if you don't understand this question, please click "select as satisfactory answer" if you have other questions, please adopt this question and send another point
25 / 16 (1-4x) & 178; = 1
1-4x = ± root (16 / 25) = ± 4 / 5
4X = 1 / 5 or 9 / 5
X = 1 / 20 or 9 / 20
25 / 16 (1-4x) & 178; = 1
(1-4x) & 178; = 16 / 25
1-4x = 4 / 5 or 1-4x = - 4 / 5
X1 = 1 / 20, X2 = 9 / 20
4X & # 178; + 8x + 1 = 0 the process of solving the equation
4x²+8x+1=0(2x)²+2*2*2x+4-4+1=0(2x+2)²=32x+2=±√3x=-1±√3/2
How to solve the equation 4x & # 178; - 4x + 1 = 0 with collocation method
4x^2-4x+1=0
x^2-x+1/4=0
x^2-2*1/2x+1/4-1/4+1/4=0
(x-1/2)^2=0
x=1/2
Fixed interval of moving axis: find the minimum value of quadratic function y = x & # 178; - 4x-4 when x ∈ [T-2, T-1]
f(x)=x²-4x-4=(x-2)^2-8
T-14, the function increases
g(t)=(t-2)^2-4(t-2)-4=t^2-8t+8
Three
Let 12n be the smallest positive integer n of an integer=______ .
12n = 23n, because 12n is an integer, the minimum positive integer value of n is 3
Let a and B be two moving points on the ellipse x ^ 2 + 5Y ^ 2 = 1, and OA ⊥ ob (o is the origin of the coordinate), find the maximum and minimum of / AB /
Let OA = m, OB = n, s and the positive angle between OA and X-axis be & then the coordinates of point a (MCOs &, MSIN &), B (nsin &, NCOs &), and two points a and B are on the ellipse, substituting into coordinates, there are (MCOs & ^ 2 + 5 (MSIN &) ^ 2 = 1, (nsin &) ^ 2 + 5 (NCOs &) ^ 2 = 1 is sorted out as 1 / m ^ 2 = cos & ^ 2 + 5sin & ^ 2 1 / N ^ 2 = Sin & ^ 2 + 5cos & ^ 2. The sum of the two formulas is 1 / m ^ 2 + 1 / N ^ 2 = 6. According to the inequality AB ^ 2 = m ^ 2 + n ^ 2, the typing is too troublesome
Adopt
Quadratic function y = 12 + 4x - X & # 178;, when x=____ Y is the best_____ The value is______
Quadratic function y = 12 + 4x - X & # 178;, when x=_ 2___ Y is the best__ Big___ The value is___ 16___
When x = 2, the maximum value of Y is 16
For a three digit number, the sum of all the digits is equal to the sum of all the digits of its square root. The product of all the digits of the three digit number is smaller than its square root. 1. What is the three digit number?
Because 102 = 100322 = 1024, the square root of this three digit number is a two digit number in 10 ~ 32, and the product of each digit of this three digit number is 1 smaller than its square root, so its square root is not 10, 20, 30
Given that the point P is any point on the ellipse x ^ 2 / 4 + y ^ 2 / 3 = 1, then the minimum distance between the point P and the line L: x + 2y-12 = 0
From image analysis, let a straight line parallel to x + 2y-12 = 0 be x + 2y-m = 0, which is tangent to the ellipse x ^ 2 / 4 + y ^ 2 / 3 = 1. Then the tangent point is the point P
From x + 2y-m = 0, we get x = m-2y. Substituting it into ellipse x ^ 2 / 4 + y ^ 2 / 3 = 1. Because it is tangent, the sorted quadratic equation has two equal real number solutions. The discriminant of root = 0
The solution is m = 4
Substituting into P coordinate (1,3 / 2)
So the minimum value is 8 root 5 / 5