If 2x2 + 5x + 1 = a (x + 1) 2 + B (x + 1) + C, then a, B, C should be () A. a=2，b=-2，c=-1B. a=2，b=2，c=-1C. a=2，b=1，c=-2D. a=2，b=-1，c=2

If 2x2 + 5x + 1 = a (x + 1) 2 + B (x + 1) + C, then a, B, C should be () A. a=2，b=-2，c=-1B. a=2，b=2，c=-1C. a=2，b=1，c=-2D. a=2，b=-1，c=2

2x2 + 5x + 1 = a (x + 1) 2 + B (x + 1) + C = AX2 + (2a + b) x + A + B + C, a = 2, 2A + B = 5, a + B + C = 1, the solution is a = 2, B = 1, C = - 2, so choose C

Square of 2x + 5x-12 = 0
Matching method

The square of 2x - 3x + 8x-12 = 0
x(2x-3)+4(2x-3)=0
(x+4)(2x-3)=0
x=-4,x=3/2

2X square - 5x + 10 = 0

A:
2x^2-5x+10=0
Discriminant = (- 5) ^ 2-4 * 2 * 10 = 25-80 = - 55

In the arithmetic sequence {an}, A6 = A3 + A8, then S9=______ ．

Let the tolerance of {an} be D, and the first term be A1. From the meaning of the question, we can get that a1 + 5D = a1 + 2D + A1 + 7d, ｜ a1 + 4D = 0, S9 = 9a1 + 9 × 82d = 9 (a1 + 4D) = 0, so the answer is 0

X + 3Y = 2.3y + Z = 4.z + 3x = 6 to solve the equation

X+3Y=2 【1】
3Y+Z=4 【2】
Z+3X=6 【3】
From [2] to [1], it is concluded that:
z-x=2 【4】
From [3] to [4], it can be concluded that:
4x=4
x=1
Substitute [1] to get:
1+3Y=2
3y=1
y=1/3
x=1
Substitute [3] to get:
Z+3=6
z=3
suoyi :x=1 y=1/3 z=3

A car consumes 112 liters of fuel per kilometer. According to this calculation, how many liters of fuel per 45 kilometers? How about 50 kilometers?

112 × 45 = 115 (L), 112 × 50 = 256 (L); answer: the fuel consumption is 115 L for 45 km, and 256 L for 50 km

The ratio of the number of angles of two complementary angles is 7:3, and the two angles are calculated

180*7/10=126
180*3/10=54

The definition field of function FX is {x, X ≠ 0}. For any x, y in the definition field, f (XY) = f (x) + F (y). It is proved that f (x) is an even function

It's easy to say,
f(xy)=f（（-x）*（-y））= f( -x)+f（-y）= f(x)+f（y）
From the step of F (- x) + F (- y) = f (x) + F (y), take x = y everywhere in the domain of definition
2F (- x) = 2F (x)

Physical and chemical properties of glacial acetic acid

Physical properties: acetic acid is a colourless liquid with strong pungent sour taste at room temperature. The melting point of acetic acid is 16.6 ℃ (289.6 K). The boiling point is 117.9 ℃ (391.2 K). The relative density is 1.05, the flash point is 39 ℃, and the explosion limit is 4% ～ 17% (volume). Pure acetic acid will freeze into ice like crystal below the melting point, so anhydrous acetic acid is also called glacial acetic acid, Its aqueous solution is weakly acidic. Acetate is also soluble in water
Chemical property: acid
The hydrogen atom of carboxyl group in carboxylic acid, such as acetic acid, can be partially ionized into hydrogen ion (proton) and released, resulting in the acidity of carboxylic acid. Acetic acid is a weak monobasic acid in aqueous solution with an acidity coefficient of 4.8, PKA = 4.75 (25 ℃), and the pH of 1mol/l acetic acid solution (similar to that of household vinegar) is 2.4, In other words, only 0.4% of acetic acid molecules are dissociated. The acidity of acetic acid makes it react with sodium carbonate, copper hydroxide, sodium phenolate and other substances. 2ch3cooh + Na2CO3 = 2ch3coona + CO2 ↑ + H2O 2ch3cooh + Cu (OH) 2 = Cu (CH3COO) 2 + 2H2O CH3COOH + c6h5ona = C6H5OH (phenol) + CH3COONa
Dimer
The crystal structure of acetic acid shows that dimer (also called dimer) is formed by intermolecular hydrogen bonding. Dimer also exists in vapor state at 120 ℃, It has been proved that carboxylic acids with smaller molecular weight, such as formic acid and acetic acid, exist as dimers in solid, liquid and even gaseous state by freezing point reduction, molecular weight measurement and X-ray diffraction. When acetic acid is dissolved in water, the hydrogen bond between dimers will break quickly. Other carboxylic acids also have similar dimerization
solvent
Liquid acetic acid is a hydrophilic (polar) protonated solvent, similar to ethanol and water. Because of its dielectric constant of 6.2, it can dissolve not only polar compounds, such as inorganic salts and sugars, but also nonpolar compounds, such as oils or molecules of some elements, such as sulfur and iodine. It can also be mixed with many polar or nonpolar solvents, such as water, chloroform, The solubility and mixability of hexane and acetic acid make them widely used in chemical industry
chemical reaction
For many metals, acetic acid is corrosive, such as iron, magnesium and zinc, which react to form hydrogen and metal acetate. Aluminum containers can be used to transport acetic acid because aluminum forms a protective layer of alumina in the air. Metal acetate can also react with acetic acid and corresponding alkaline substances, such as the most famous example: the reaction of baking soda with vinegar, Mg (s) + 2ch3cooh (AQ) → (CH3COO) 2mg (AQ) + H2 (g) NaHCO3 (s) + CH3COOH (AQ) → CH3COONa (AQ) + CO2 (g) + H2O (L) acetic acid can take place the typical chemical reaction of common carboxylic acid. In particular, ethanol can be reduced to form acetyl chloride through nucleophilic substitution mechanism, Similarly, acetic acid can also be converted into esters or amino compounds. For example, acetic acid can react with ethanol in the presence of concentrated sulfuric acid to form ethyl acetate (this reaction is reversible and belongs to the esterification reaction in substitution reaction), Acetic acid decomposes to form methane and carbon dioxide or ketene and water
identify
Acetic acid can be identified by its odor. If ferric chloride (III) is added, the product is dark red and will disappear after acidification. Acetic acid can also be identified by this color reaction. Acetic acid reacts with arsenic trioxide to form arsenic trioxide, and acetic acid can be identified by the odor of the product

The first measurement of sound propagation speed in water was carried out on Lake Geneva in 1827. The distance between the two ships was 14km. The experimenter on one ship put a bell into the water. When he rang the bell, the gunpowder on the ship glowed at the same time. The experimenter on the other ship put a listener into the water. He saw the gunpowder glowing. After 10s, he heard the underwater bell and calculated the sound What is the propagation speed in water?

It can be seen from the meaning of the title that seeing the gunpowder glowing and hearing the sound after 10s, it can be approximately considered that the time taken for the sound to travel 14km in the water is t = 10s, v = st = 1.4 × 104m10s = 1400m / s, a: the propagation speed of the sound in the water is 1400m / s