If the sum of the coefficients in the expansion of the 9th power of (AX's Square-1 / x) is equal to 1, then a =?

If the sum of the coefficients in the expansion of the 9th power of (AX's Square-1 / x) is equal to 1, then a =?

When x = 1, the value of each term is equal to its coefficient
So the sum of coefficients is the value of (AX & sup2; - 1 / x) ^ 9 when x = 1
So (A-1) ^ 9 = 1
a-1=1
A=2
The square of (a minus 2) x plus ax plus 1 equals 0
solve equations,
(A-2) x ^ 2 + ax + 1 = 0 (1) if A-2 = 0, i.e. a = 2, the original equation is univariate linear equation 2x + 1 = 0, the solution is x = - 1 / 2 (2) if A-2 ≠ 0, i.e. a ≠ 2, the original equation is univariate quadratic equation (A-2) x ^ 2 + ax + 1 = 0, Δ = a ^ 2-4 (A-2) = a ^ 2-4a + 8 = (A-2) ^ 2 + 4 > 0. According to the root formula, we get x1,2 = (- a ± √Δ) / 2 (A-2) = [- a
① A = 0, ax + 1 = 0, x = - 1 / A
② A ≠ 0 (A-2) x & # 178; + ax + 1 = 0 △ = A & # 178; - 4 (A-2) = 0
Let a, B, C, x, y, Z be real numbers, if a ^ 2 + B ^ 2 + C ^ 2 = 25, x ^ 2 + y ^ 2 + Z ^ 2 = 36, ax + by + CZ = 30, find the value of (2007a + 5B + 8C) / (2007x + 5Y + 8Z)
Related to multiplication and division of integers
From Cauchy inequality (a ^ 2 + B ^ 2 + C ^ 2) (x ^ 2 + y ^ 2 + Z ^ 2) > = (AX + by + CZ) ^ 2, when a / x = B / y = C / Z, take the equal sign (a ^ 2 + B ^ 2 + C ^ 2) (x ^ 2 + y ^ 2 + Z ^ 2) > = (AX + by + CZ) ^ 2, so 25 * 36 > = 30 ^ 2. Obviously, take the equal sign here, so a / x = B / y = C / z > 0, so a ^ 2 / x ^ 2 = B ^ 2 / y ^ 2 = C ^ 2 / Z ^ 2 = (a ^ 2 + B
a^2+b^2+c^2=25 x^2+y^2+z^2=36 ax+by+cz=30 (a+b+c):(x+y+z)=?
(a+b+c):(x+y+z)=5:6
Cauchy inequality
(a^2+b^2+c^2)(x^2+y^2+z^2)>=(ax+by+cz)^2
The equal sign holds if and when
a/x＝b/y=c/z
25*36=30*30
So the equal sign holds
a/x＝b/y=c/z＝(a+b+c)/(x+y+z)=5/6
It's an old question
If the range of function f (x) = log2 (x2-2ax + 3) is r, the value range of a is obtained
T = x2-2ax + 3 can take all positive numbers
　　⊿>=0,
That is 4A ^ 2-12 > = 0,
　　a^2>=3,
The value range of a is (- ∞, - √ 3] ∪ [√ 3, + ∞)
Given that the image of power function f (x) = xm2-2m-3 (x belongs to Z) is symmetric about y axis and there is no intersection between X axis and Y axis, the analytic expression of function f (x) is obtained
If the image of power function f (x) = x ^ m2-2m-3 (M belongs to Z) is symmetric about y axis and there is no intersection between X axis and Y axis, then m2-2m-3 ＜ 0, the solution is - 1 ＜ m ＜ 3. (M belongs to integer z) m only takes 0,1,2
Finding the maximum value of the function f (x) = x2-2ax-1 in the interval [0,2]
f(x)=(x-a)²-a²-1
It is necessary to discuss the distance between the axis of symmetry and the end point of the interval to get the maximum value
That is, a and interval Center 1
The relationship between the axis of symmetry and the interval should be discussed when seeking the minimum value
When a ≤ 0, f (x) increases on [0,2]
f(x)min=f(0)=-1,f(x)max=f(2)=3-4a
When 0
If the definition of the function is ⊸ B, then ⊸ a = B ⊸ B X B, then ⊸ a ⊸ B X B X B X a X B X B X B X B X B X B______ .
From a ⊗ B = B, a ≥ Ba, a < B, f (x) = x ⊗ (2-x) = 2 − x, X ≥ 1 x, x < 1, ⊗ f (x) is an increasing function on (- ∞, 1), a decreasing function on [1, + ∞), and ⊗ f (x) ≤ 1, then the range of F (x) is: (- ∞, 1), so the answer is: (- ∞, 1]
It is known that the range of the function ax & sup2; - 2aX + 2 + B (a > 0) + on the interval [2,3] is [2,5]
(1) If the function g (x) = f (x) - (M + 1) x is a monotone function on [2,4], the value range of M is obtained
F (x) = ax & sup2; - 2aX + 2 + B, the axis of symmetry is x = 1. The opening is upward. It is an increasing function on [2,3], so f (2) = 4a-4a + 2 + B = 2F (3) = 9a-6a + 2 + B = 5, B = 0, a = 1F (x) = x ^ 2-2x + 2 (2) g (x) = x ^ 2-2x + 2 - (M + 1) x = x ^ 2 - (M + 3) x + 2, the axis of symmetry is x = (M + 3) / 2. It is a monotone function on [2,4]
(1) a=1 b=0
(2) m∈(-∞,1]∪[5，+∞)
If we define the operation a ⊗ B = B, a ≥ Ba, a < B, then the range of function f (x) = x ⊗ (2-x) is______ .
From a ⊗ B = B, a ≥ Ba, a < B, f (x) = x ⊗ (2-x) = 2 − x, X ≥ 1 x, x < 1, ⊗ f (x) is an increasing function on (- ∞, 1), a decreasing function on [1, + ∞), and ⊗ f (x) ≤ 1, then the range of F (x) is: (- ∞, 1), so the answer is: (- ∞, 1]