It is known that the function f (x) is a decreasing function in the domain (- 1,1), and f (1-A) - f (a ^ 2-1)

It is known that the function f (x) is a decreasing function in the domain (- 1,1), and f (1-A) - f (a ^ 2-1)

f(1-a)-f(a^2-1)
You can get it from the question
-1
Known function FX known function FX in the domain (- 1,1) is a decreasing function, and f (1 + a) + F (1-A & # 178;) to find the value range of real number a!
The odd function f (x) is a decreasing function in the domain (- 1,1), and f (1 + a) + F (1-A & # 178;) > 0,
Then f (1 + a) > - f (1-A ^ 2) = f (a ^ 2-1),
∴-1
Find the equation of the line L with the circumference of 9 and the slope of − 43
Let the equation y of line L = - 43x + B, then the intersection points (34B, 0), (0, b), ∵ of line L and two coordinate axes and the circumference of triangle enclosed by two coordinate axes are 9, ∩ 34B | + | B | + (& nbsp; 3b4) & nbsp; 2 + B2 = 9, 3 | B | = 9, ∩ B = ± 3. The equation of line L: y = - 43x + 3, or y = - 43x-3. That is 4x + 3y-9 = 0, or 4x + 3Y + 9 = 0
It is known that the set a = {a (x + a) / (x ^ 2-2) = 1 has a unique real solution}, and the set a is represented by enumeration
A = radical 2, a = - radical 2
Consider the discriminant. 9 + 4A = 0. A =?
Without formula editor, you can make do with it. No more discussion
If the line L: ax + by + 1 = 0 (a > 0, b > 0) always bisects the circumference of the circle M: x2 + Y2 + 8x + 2Y + 1 = 0, then the minimum value of 1A + 4b is______ .
The equation of the circle is (x + 4) 2 + (y + 1) 2 = 16, the coordinate of the center of the circle is (- 4, - 1) ∵ the line L: ax + by + 1 = 0 (a > 0, b > 0) always bisects the circumference of the circle M: x2 + Y2 + 8x + 2Y + 1 = 0 ∵ the line L passes through the center of the circle, that is - 4a-b + 1 = 0 ∵ 4A + B = 1 ∵ 1A + 4B = (4a + b) (1a + 4b) = 8 + 16ab + BA ≥ 8 + 216ab · Ba = 16 (if and only if 16ab = BA), so the answer is: 16
It is known that the set a = {a | x + A / x ^ 2-2 = 1 has a unique real solution}. We try to express the set a by enumeration. Why can we make x ^ 2-2 = 0?
Won't this make x + A / x ^ 2-2 meaningless?
The formula x ^ 2-2 given by the title appears as the denominator, then it must be meaningful, that is, x ^ 2-2 = 0 is not tenable, this is the rule
(x + a) / (x ^ 2-2) = 1, which is changed into: x ^ 2-x-2-a = 0, the formula has a unique real solution
So △ = 1-4 (- 2-A) = 9 + 4A = 0, a = - 4 / 9
Set a = {- 4 / 9}
The title is (x + a) / (x ^ 2-2) = 1. Yes... First of all, we have to consider 1. (x ^ 2-2) = 0 2. (x ^ 2-2) ≠ 0. In both cases, we have to consider 1. (x ^ 2-2) = 0, the numerator must have an equation that can make the denominator cross off the 0 factor At this time, x = ± √ 2... Expands
Do you mean (x + a) / (x ^ 2-2) = 1
If the minimum value of the circumference of the line (y 2 + 0 + 2 b) is always y 2 + 0, then the minimum value of the circumference of the line (y 2 + 0 + 2 b) is y 2 + 0______ .
The straight line ax + by + 1 = 0 (a > 0, b > 0) always bisects the circumference of the circle x2 + Y2 + 2x + 2Y = 0, and the center coordinates of the circle are (- 1, - 1), so a + B = 1, so 1A + 1b = (a + b) (1a + 1b) = 2 + Ba + ab ≥ 4, if and only if Ba = AB, that is, a = b = 1, the equal sign holds, so the minimum value of 1A + 1b is 4; so the answer is: 4
Given that the set a = {a (x + a) / (XX-2) = 1 has a unique real number solution}, the set a is represented by enumeration
(x + a) / (x ^ 2-2) = 1 has unique real solution
x+a=x^2-2
x^2-x-2-a=0
1) There are equal roots: delta = 1 + 4 (2 + a) = 0, a = - 9 / 4, then x = 1 / 2
2) There are unequal roots, but one of them is increasing root √ 2 or - √ 2. In this case, delta > 0, that is a > - 9 / 4
Substituting √ 2 into the equation: 2 - √ 2-2-a = 0, a = - √ 2,
Substituting - √ 2 into the equation: 2 + √ 2-2-a = 0, a = √ 2
A = {- 9 / 4, √ 2, √ 2}
It is known that the parabolic equation is y2 = 2x. On the y-axis, the line L with intercept 2 intersects the parabola at two points m and N, and O is the origin of the coordinate. If om ⊥ on, the equation of the line L is obtained
Let the equation of line l be y = KX + 2 (1 min) and eliminate X by y2 = 2XY = KX + 2, then: ky2-2y + 4 = 0 (3 min) ∵ the intersection of line L and parabola ∵ K ≠ 0 △ = 4 − 16K ∵ 0 ∵ K ＜ 14 & nbsp; and & nbsp; K ≠ 0 (5 min) let m (x1, Y1), n (X2, Y2), then y1y22 = 4K (6 min) and x1x2 = y212 & nbsp;; · & nbsp; y222 = 4k2 (8 min) ≁ om ⊥ on ∵ x1x2 + y1y2 = 0 (10 min), that is & nbsp; The equation of k = - 1 is y = - x + 2 (12 points)
It is known that the set a = {a | x + A / x ^ 2-2 = 1 has a unique real solution}. The enumeration method is used to represent the set a
Set a = {- 9 / 4, √ 2, - √ 2}
How does the positive and negative root sign 2 come out
Why there are so many answers on the Internet, a = positive and negative root sign 2? How did it come out?
The problem is to write all a, a satisfy the equation x + A / x ^ 2-2 = 1 and have unique real solution
According to many years of experience, I think (x ^ 2-2) as a whole is the denominator, otherwise - 2 can be directly moved to the right
(1) A = 0, the original equation is equivalent to x = 1, satisfying the condition;
(2) A ≠ 0, the original equation is equivalent to x ^ 3-x ^ 2-2x + A + 2 = 0, and x ^ 2-2 ≠ 0, let x ^ 3-x ^ 2-2x + A + 2 = (x + a) (x ^ 2 + BX + C), where a, B and C are undetermined constants, then expand the right side, and compare with the left side: A-B = 1, ab-c = 2, - AC = a + 2, if the cubic equation has a unique real solution, then the quadratic equation x ^ 2 + BX + C = 0 has no real solution, that is B ^ 2-4c