![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given that one root of the real coefficient equation x2 + ax + 2B = 0 is greater than 0 and less than 1, and the other root is greater than 1 and less than 2, the value range of B − 2A − 1 is () A. （14，1）B. （12，1）C. （-12，14）D. （0，13）
Let f (x) = x2 + ax + 2B, from the topic meaning: F (0) > 0f (1) < 0f (2) > 0, i.e. b > 0A + 2B + 1 < 0A + B + 2 > 0, draw the plane region represented by the above inequality group in the coordinate system AOB, and the plane region represented by the topic meaning and constraint condition is the shadow part (excluding the boundary). The geometric meaning of the objective function B − 2A − 1 is the straight line connecting two points (x, y) and point C (1, 2) in the feasible region According to the plane area, it is easy to find the maximum value of B − 2A − 1 is KBC = 1, and the minimum value is KAC = 14, so B − 2A − 1 ∈ (14,1), so a is selected
The real coefficient equation f (x) = x2 + ax + 2B = 0 has one root in (0,1) and the other root in (1,2). Find: (1) the range of B − 2A − 1; (2) the range of (A-1) 2 + (b-2) 2; (3) the range of a + B-3
If we know that f (0) > 0f (1) < 0f (2) > 0, then the constraint condition is: b > 01 + A + 2B < 02 + A + b > 0. Its feasible region is a triangle composed of a (- 3,1), B (- 2,0) and C (- 1,0). The active region of (a, b) is a triangle ABC, where (1) let k = B − 2A − 1, then the expression B − 2A − 1 represents the slope of the straight line passing through (a, b) and (1,2), and the slope kmax = 2 − 01+ 1 = 1, Kmin = 2 − 11 + 3 = 14, so the answer is: (14, 1) (2) let P = (A-1) 2 + (b-2) 2, then the expression (A-1) 2 + (b-2) 2 represents the square of the distance between (a, b) and (1, 2), the square of the distance Pmax = (- 3-1) 2 + (1-2) 2 = 17, Pmin = (- 1-1) 2 + (0-2) 2 = 8, the answer is: (8, 17); (3) let z = a + B + 3, that is, the maximum value of the objective function Z is required In the rectangular coordinate system, the image of B = - A + (Z + 3) can be obtained by pushing | Z + 3 | units up or down the image of B = - A + (Z + 3) | Zmax = - 1 + 0-3 = - 4, Zmin = - 3 + 1-3 = - 5, so the answer is: (- 5, - 4)
There are 36 students in the art group of the experimental primary school, and the number of girls is 80% of that of boys. How many boys and girls are there in the art group?
Boys: 36 △ 1.8, = 20; girls: 36-20 = 16 or 20 × 80% = 16; a: there are 20 boys and 16 girls
What is the square root of 31.4 0.0314 0.314 3140
If a, B and C jointly buy a TV set, half of what a pays is equal to one third of what B pays and three seventh of what C pays. It is known that C pays 98% more than a
How much is the price of this printer?
A: B = (1 / 3): (1 / 2) = 2:3 = 6:9
B: C = (3 / 7): (1 / 3) = 9:7
A: B: C = 6:9:7
98 △ ((7 / 22) - (6 / 22)) = 2156 (yuan)
The price of this printer is 2156 yuan
The division of two negative numbers is equal to the division of their opposite numbers
Yes
For example, if the opposite number of - 5 △ 5 = 1 - 5 is 5, then 5 △ 5 = 1
So is the fraction - 4 / 5 △ 4 / 5 = 1 - 4 / 5. If the opposite number is 4 / 5, then 4 / 5 △ 4 / 5 = 1
The ratio of the number of a, B and C is 5:6:7. If the number of C is 4 larger than that of a, then the number of B is () a.10 b.12 C
The ratio of the number of a, B and C is 5:6:7. If the number of C is 4 larger than that of a, then the number of B is ()
A.10 B.12 C.14
A
Let the equation sin (2x + π 6) = K + 12 have two different roots α, β in [0, π 2]. Find the value of α + β and the range of K
∵ x ∈ [0, π 2], ∵ (2x + π 6) ∈ [π 6, 7 π 6]. ∵ the equation sin (2x + π 6) = K + 12 of X has two different roots α, β, ∵ 12 = sin π 6 ≤ K + 12 < 1 in [0, π 2]. The solution is 0 ≤ K < 1, ∵ α + β = 2 × π 2 = π
2 / 3 of a number is 3 / 4, and 1 / 5 of this number is?
3/4÷2/3×1/5=9/40
Two thirds of a number is three fourths, and one fifth of a number is nine fourths
To solve the ternary linear equations 2x + Z = 3 3x + Y-Z = 8 x + 3Y + 2Z = 3? To solve the process!
2x+z=3 (1)
3x+y-z=8 (2)
x+3y+2z=3 (3)
(2) 3 - (3)
8x-5z=21 (4)
(1) 5 + (4)
18x=36
x=2
Substituting (1) to get:
z=-1
Substituting (2) to get:
6+y+1=8
y=1
Therefore, the solution of the equations is: x = 2; y = 1; Z = - 1
RELATED INFORMATIONS
- 1. If one root of the real coefficient equation x * x + ax + 2B = 0 is greater than 0 and less than 1, and the other root is greater than 1 and less than 2, what is the value range of (b-2) / (A-1)
- 2. For the equation (1 + k) x & # 178; + (1 + k) y & # 178; + 4 (k-1) x + 2 (2k-1) y + 4-8k = 0, take any two values of K1 and K2 which are not equal to - 1, whether the curve corresponding to the equation is a circle? If not, explain the reason
- 3. 3x=5y 2y-2=x
- 4. X-5y = - 3, 3x + 2Y = - 9,
- 5. (x + 5x + 3) (x + 5x-2) - 6 factorization,
- 6. It is known that the cube of (2x-1) = the cube of AX + the square of BX + CX + D. if the value of a + B + C + D, the idea of x =? Is the simplest
- 7. Given that the cube of (2x-1) = the cube of AX + the square of BX + CX + D, if the value of a + B + C + D, then the following () idea is the most simple A. substituting x = 1 into B. substituting x = 1 / 2 into C. substituting x = 0 into D. substituting x = - 1 into D
- 8. Let f (x) = x ^ 2, G (x) = 2 ^ x find f (g (x)) and G (f (x))
- 9. Let g (x) = 2x + 3, G (x + 2) = f (x), then f (x)=______ ．
- 10. Mathematical problem f (x + 1) = 2x ^ 2 + 1, then f (x)=
- 11. Set up equations or equations to solve application problems: a sports goods store predicted that a certain brand of sportswear would sell well, so it bought a batch of sportswear with 32000 yuan, which was out of stock soon after it came into the market. The store bought the second batch of sportswear with 68000 yuan, which was twice the quantity of the first batch, but the price of each set was 10 yuan more. How many sets of sportswear did the store buy in two times?
- 12. It is known that if one root of the equation x2 + (A-1) x + (A-2) = 0 is smaller than 1, then the value range of a is smaller If one of the roots of equation x2 + (A-1) x + (A-2) = 0 is smaller than 1 and one of the roots is larger than 1, then the value range of a is larger
- 13. It is known that the equation (m ^ 2-4m + 5) x ^ 2 + (2m + 1) X-1 = 0 about X. proof: no matter what the value of M is, the equation is a univariate quadratic equation about X 2. No matter what the value of M is, the equation always has two unequal real roots
- 14. ④ Known: (x-2013) (2014-x) = m, find the value of (x-2013) 2 + (2014-x) 2 [expressed by the algebraic formula containing M]
- 15. 8 ^ 2013 times (- 0.125) ^ 2012=___ ?
- 16. 1 + 2 + 3 +,,, + 2012 + 2013 Simple, clear. Thank you
- 17. (- 2 radical 2) square - (radical 2 + 1) square + (radical 2-1) negative power Please help me
- 18. If a and B are opposite to each other, C and D are reciprocal to each other, and the absolute value of M is 1, find the value of 2014 (a + b) - CD + 2014m
- 19. If x (Y-1) - Y (x-1) = 4, find the value of x2 + Y22 − XY
- 20. Given x + y = 2, xy = - (1 / 2), find the value of X (x + y) &# 178; (1-y) - x (y + x) &# 178