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If inequality (5-a) x2-6x + A + 5 > 0 holds for any real number x, then the value range of real number a is______ ．
When a ≠ 5, the (5-a) x2-6x + A + 5 image is a parabola, and its function value must be positive, then the opening is upward and there is no intersection with the X axis. 5 − a ＞ 0 △ 0, the solution is - 4 ＜ a ＜ 4, and a ≠ 5. On the other hand, when a = 5, the inequality can be transformed into - 6x + 10 ＞ 0, and it is not tenable when a = 5
If - 3a is positive, then the solution set of inequality X / 3 > ax / 2-2 / 2 is positive
From - 3A > 0
a < 0
x/3 > ax/2 - 1
2x > 3ax - 6
(3a - 2)x < 6
x > 6/(3a - 2)
Given that the system of inequalities x-3 (X-2) x has a solution, the range of real number a is obtained
x-3(x-2)4x
2x4
On the inequality system of x x ^ 2-x-6 > 0; 2x ^ 2 + (7 + 2a) x + 7a
Solving inequality x ^ 2-x-6 > 0 (reduced to (x-3) (x + 2) > 0)
Get x > 3 or X
The solution set of inequality (x ^ 2-7x + 12) (x ^ 2 + 1) > 0 is
(x^2-7x+12)(x^2+1)>0
X ^ 2 + 1 is always greater than 0,
So as long as (x ^ 2-7x + 12) > 0
We get (x-4) (x-3) > 0, x > 4 or X
Who will teach me
1, solve inequality x2 + X-12
Question 1: x2 + X-12
The solution set of quadratic inequality x2-x-2 > 0 is ()
A. （∞，-1）∪（2，+∞）B. （-1，2）C. （-∞，-2）∪（1，+∞）D. （-2，1）
Inequality x2-x-2 ＞ 0 is transformed into (X-2) (x + 1) ＞ 0, and the solution is x ＞ 2 or X ＜ - 1. The solution set of inequality x2-x-2 ＞ 0 is (- ∞, - 1) ∪ (2, + ∞)
Let m = {x | x2 + 2x-15
M = (x-3) (x + 5) 0
∴M= -5
Solving quadratic inequality of one variable: - x2 + 2x + 3 > 0
-X2 is the square of - X
-x2+2x+3>0
x2-2x-3
When k is a value, the solution set of the quadratic inequality x2 + (k-1) x + 4 > 0 is empty
∵ f (x) = x ^ 2 + (k-1) x + 4 image opening up ∵ no matter what value K takes, there is always a function image above the X axis, so no matter what value K takes, the solution of the inequality will not be an empty set
RELATED INFORMATIONS
- 1. The solution of inequality (6x-x2-x3) (x2-7x + 10) is greater than 0
- 2. Shanghai Science Edition mathematics basic training 8.5 expand space answer
- 3. How to solve the sum of X + 1 of quadratic inequality x with one variable less than or equal to 3?
- 4. When the linear function y > 0, the value of X is a linear inequality of one variable_______ The solution set of the model; When a linear function y
- 5. If (M + 1) x | m | + 2 ＞ 0 is a linear inequality with respect to x, then the value of M is________ ．
- 6. A T-shirt is priced at 200 yuan and can sell 500 pieces per month. According to the survey, 50 more T-shirts can be sold for every 3 yuan price reduction. There are 1000-1200 T-shirts at present. If you want to sell them out in a month, how much should you sell?
- 7. A mathematical problem about the linear inequality of one variable? When a supermarket purchases a batch of fruits, the quality loss is 5% in the transportation process, assuming that the supermarket does not include other costs (1) If the supermarket takes 5% of the purchase price as the selling price, please use the calculation to explain whether the supermarket is losing money (2) If the supermarket wants to make at least 20% profit, what is the minimum price increase of this fruit? (the result is accurate to 0.1%) It's a simple inequality
- 8. It is known that f (x) = asin (π x + α) + bcos (π X - β), where α, β, a and B are non-zero real numbers. If f (2012) = - 1, then f (2013) =? [the answer is 1]
- 9. If a belongs to a, then (1 / 1-A) belongs to a, and 1 does not belong to a.1). If 2 belongs to a, and a has three elements, find the set a 2) Verification: if a belongs to a, then (1-1 / a) belongs to a
- 10. Proof: when m is a real number, at least one of the quadratic equation x2-5x + M = 0 and the equation 2x2 + x-6-m = 0 has a real root
- 11. Solve the following inequality. (1) x2-7 + 12 > 0 (2) - x2-2x + 3 ≥ 0 (3) x2-2x + 1 < 0 (4) x2-2x + 12 < 0
- 12. What is the maximum distance between circle x2 + y2-2x + 4Y + 4 = 0 and straight line 3x-4y + 9 = 0?
- 13. The distance from the point (- 1,2) to the line 3x + 4y-7 = 0 is___
- 14. If the distance between two parallel lines 3x + 4Y + 5 = 0 and + 6x + ay + 30 = 0 is D, then a + D =? Find the specific process,
- 15. Find a point m on the parabola x ^ 2 = 1 / 4Y, so that the distance from m to the straight line y = 4x-5 is the shortest
- 16. It is known that P is on the straight line L: x + Y-1 = 0 and Q is on the circle C: (X-2) 2 + (Y-2) 2 = 1. (1) make the tangent PM, PN and tangent point of circle C through P It is known that P is on the straight line L: x + Y-1 = 0 and Q is on the circle C: (X-2) 2 + (Y-2) 2 = 1. (1) through P, make the tangent PM, PN of circle C, and the tangent points are m, N, and find the minimum value of cos ∠ MPN. (2) through P, make the tangent PM, PN of circle C, and the tangent points are m, N, and find cos ∠ MPN ≤ 35, calculate the value range of abscissa of point P
- 17. If the moving point P (x0, Y0) moves on the curve y = 2x & # 178; + 1, find the trajectory equation of the midpoint of the line between P and point (0, - 1)
- 18. It is known that circle C passes through point a (- 2,0) and point (0,2), and the center of circle is on the straight line y = x, and there is a straight line L = KX + 1 intersecting with circle C at two points P and Q It is known that circle C passes through point a (- 2,0) and point (0,2), and the center of circle is on the straight line y = x, and there is a straight line L = KX + 1 intersecting with circle C at P and Q. The equation of circle C is obtained
- 19. Given that x ^ 2 + y ^ 2 = 1 and the line y = 2x + m intersect a and B, and the angles between OA, OB and the positive direction of X axis are a and B respectively, it is proved that sin (a + b) is a fixed value
- 20. It is known that circle C: x ^ 2 + y ^ 2-2x + 4y-4 = 0. Is there any symmetry between two points a and B on circle C about the straight line y = kx-1, and the circle with diameter AB passing through the origin?