Given that G (x) = - x2-3, f (x) is a quadratic function, f (x) + G (x) is an odd function, and when x ∈ [- 1, positive infinity], the minimum value of F (x) is 1, find the expression of F (x) -X2 is the square of negative X

Given that G (x) = - x2-3, f (x) is a quadratic function, f (x) + G (x) is an odd function, and when x ∈ [- 1, positive infinity], the minimum value of F (x) is 1, find the expression of F (x) -X2 is the square of negative X

Because f (x) is a quadratic function, Let f (x) = ax & sup2; + BX + C
First, f (x) + G (x) is an odd function. Let t (x) be the odd function
So t (0) = 0, and G (x) = - X & sup2; - 3
Substituting t (0) = f (0) + G (0) = C-3 = 0
∴c=3 → f（x）=ax²+bx+3
The odd function T (x) has t (1) + T (- 1) = 0
Substituting: t (1) + T (- 1) = f (1) + G (1) + F (- 1) + G (- 1)
=a+b+3-4+a-b+3-4
=2a-2
=0
A = 1 → f (x) = x & sup2; + BX + 3 the opening of the image is upward, and the symmetry axis is x = - B / 2
(discuss with image classification)
① The axis of symmetry is on the left side of - 1, that is, when x = - B / 2 ＜ - 1 → B ＞ 2
The image is obtained when x ∈ [- 1, positive infinity] is the minimum x = - 1,
Substituting f (- 1) = 1-B + 3 = 1, B = 3 > 2, it is true;
② When the symmetry axis is between [- 1, positive infinity], when - 1 ≤ - B / 2 ≤ 2 → 2 ≥ B ≥ - 4
Image x = - B / 2 is the smallest
Substituting f (- B / 2) = B & sup2 / 4-b & sup2 / 2 + 3 = - B & sup2 / 4 + 3 = 1 → B = ± 2 √ 2 (± 2 root sign 2)
If 2 ≥ B ≥ - 4, 2 √ 2 ＞ 2, rounding off, - 2 √ 2 is consistent, it is tenable;
③ The axis of symmetry is on the right side of 2, that is, when side x = - B / 2 ＞ 2 → B ＜ - 4
The image is obtained when x ∈ [- 1, positive infinity] is the minimum x = 2,
Substituting f (2) = 4 + 2B + 3 = 1b = - 3 ＞ - 4, rounding off
In conclusion, the value of B is 3 or - 2 √ 2
So f (x) = x & sup2; + 3x + 3 or F (x) = x & sup2; - 2 √ 2x + 3

Given that G (x) = - x2 + 3, f (x) is a quadratic function, when x ∈ [- 1,2], the minimum value of F (x) is 1, and f (x) + G (x) is an odd function, the expression of F (x) is obtained

Let f (x) = ax & sup2; + BX + C (a ≠ 0)
F (x) + G (x) is an odd function
=> [f(x）+g（x）]+[f(-x)+g(-x)]=0
Take x = 0
=>[f(0）+g（0）]+[f(0)+g(0)]=0
=> c=-3
Similarly, take x = 1
=> a+c=-2
=>a=1
∴ f（x）=x²+bx-3
When x belongs to [- 1,2], the minimum value of F (x) is 1
We discuss - B / 2 on [- 1,2]
When - B / 2 = 2, the minimum value of F (x) is f (- 1) = - 2 - B = 1 = > b = - 3
When - 1

What factors are related to the resistance of conductor
Connect the battery pencil lead and the small light bulb in series with a wire, adjust the length of the pencil lead into the circuit, so that the small light bulb just doesn't shine. Light the candle with a match and heat it near the lead lead pencil lead. After a while, I find that the small light bulb lights up gradually. Blow out the candle, and I find that the small light bulb also goes out slowly

The resistance of a conductor is generally related to the following factors: conductor length, cross-sectional area, material and temperature
The longer the conductor, the greater the resistance; the smaller the cross-sectional area, the greater the resistance; as for the material, it depends on the actual situation
The phenomenon mentioned by the landlord is related to the temperature of the conductor. In that case, heating the conductor to raise the temperature will reduce the resistance, so the light bulb will turn on, and vice versa

An applied problem of solving equation
Grandma made a noodle fish for her mother. The head length of the noodle fish is 3cm, the body length is equal to the head length and tail length, and the tail length is equal to half of the head length and body length. Can you work out the total length of the noodle fish?

If the tail length is x cm, the body length is (3 + x) cm
X = 3 + (3 + x) / 2
The solution is x = 9
So the total length is 3 (head) + 12 (x + 3; body) + 9 (tail) = 24 (CM)

How can we calculate how long a household appliance uses one kilowatt hour electricity

One kilowatt hour (1000 watt hours) is the unit of electrical work. To work out how long a household appliance uses one kilowatt hour, you must know the power of the appliance. For example, a 100 watt bulb works for 10 hours, which is 1000 watt hours (1 kilowatt hour), How long does a 25 watt bulb work for one degree of electricity (1000 watt hours)

The decomposition factor is: ab2-2ab + a=______ ；②（a+b）2-6（a+b）+9=______ ．

① Ab2-2ab + a = a (b2-2b + 1) = a (B-1) 2; ② (a + b) 2-6 (a + b) + 9 = (a + B-3) 2

What is the maximum output power of 72V 120ah battery? How to calculate the maximum output power of battery?

The maximum output power of power battery is calculated according to the maximum current 1C discharge
For example, the maximum output power of 72v120ah battery is 72 * 120 = 8.64kw
Of course, the maximum power in actual use can exceed this value, but that will cause irreversible damage to the battery

7 / 9 △ 11 / 5 + 2 / 9 × 5 / 11 help me with the simple calculation,
5 / 12 △ 8 + 1 / 8 × 7 / 12
24 × (3 / 8 + 5 / 6)
(2 / 11 + 3 / 22 + 4 / 33) × 66
It's all about simple calculation,

7 of 9 △ 11 of 5 + 2 of 9 × 11 of 5 = 7 / 9 × 11 / 5 + 2 / 9 × 11 / 5 = (7 / 9 + 2 / 9) × 11 / 5 = 1 × 11 / 5 = 5 of 11 / 512 △ 8 + 8 of 1 × 12 of 7 = 5 / 12 × 1 / 8 + 7 / 12 × 1 / 8 = (5 / 12 + 7 / 12) × 1 / 8 = 1 × 1 / 8 = 1 / 824 × (3 of 8 + 5 of 6) = 24 × 3 / 8 + 24 × 5 / 6 = 9 + 20 = 29 (11

The generator terminal voltage is 220 V, and the output power is 110 kW. If the user needs to get at least 100 KW electric power, the resistance of the transmission line should not be more than how many ohm

First, 100kW is converted into w = 100000w. Finally, by the formula r = U2 / P and the known voltage is 200V, the power is 100000w, and finally r = 220 * 220 / 100000 = 0.484, the electric power can be 100kW when the resistance is not more than 0.484 ohm

There are three classes of 45 students in grade five of a school. The number of boys in class five (1) is equal to that of girls in class five (2)···
There are three classes of 45 students in grade five of a school. The number of boys in class five (1) is equal to that of girls in class five (2). Five out of nine students in class five (3) are boys

If the number of boys in class 5 (1) is equal to that of girls in class 5 (2), then the number of girls in class 1 is equal to that of boys in class 2
There are 45 boys and 45 girls in class 1.2
Class 3 boys = 45 × 5 / 9 = 25
Total number of boys = 45 + 25 = 70