It is known that a, B, C and D are four different integers, and ABCD = 25

It is known that a, B, C and D are four different integers, and ABCD = 25

The four numbers can only be 1, - 1, 5, 5, - 5, 5, - 5, 5, 5, 5, 5, 5, \\\\\\\\\abcd = 25, the four numbers can only be 1, - 1, B, B, C, C, C, C, C, C, C, C, D, D, and ABCD = 25, \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\= 25 ，… The values of ABCD are only 125, 1 and 25

How to calculate or express the coefficients of polynomials?

Addition and subtraction of coefficients of similar terms

If the arc length of 60 ° central angle is 10 cm, then the circumference of the circle is______ Cm

(360 ° / 60 °) × 10, = 6 × 10, = 60 (CM). Answer: the circumference of the circle is 60 cm

Summary and comparison of arithmetic arithmetic series formula in senior high school mathematics

If a sequence starts from the second term, and the difference between each term and its previous term is equal to the same constant, the sequence is called the arithmetic sequence, and the constant is called the tolerance of arithmetic sequence. The tolerance is usually expressed by the letter D
The general formula of arithmetic sequence is as follows:
an=a1+(n-1)d (1)
The first n terms and formula are as follows:
Sn = Na1 + n (n-1) d / 2 or Sn = n (a1 + an) / 2 (2)
It can be seen from formula (1) that an is a function of degree (D ≠ 0) or a constant function (d = 0) of N, and (n, an) is arranged on a straight line. From formula (2), Sn is a quadratic function (D ≠ 0) or a function of degree (d = 0, A1 ≠ 0) of N, and the constant term is 0
In the arithmetic sequence, the mean of arithmetic: AR, am + an = 2AR, so AR is the mean of arithmetic of AM and an
The relationship between any two terms am and an is as follows:
an=am+(n-m)d
It can be regarded as the generalized general term formula of arithmetic sequence
From the definition of arithmetic sequence, the general term formula, the first n terms and the formula, we can deduce that:
a1+an=a2+an-1=a3+an-2=… =ak+an-k+1,k∈{1,2,… ,n}
If m, N, P, Q ∈ n *, and M + n = P + Q, then
am+an=ap+aq
Sm-1=(2n-1)an,S2n+1=(2n+1)an+1
Sk,S2k-Sk,S3k-S2k,… ,Snk-S(n-1)k… Or arithmetic sequence, etc
Sum = (first item + last item) * number of items △ 2
Number of items = (last first item) △ tolerance + 1
First term = 2 and △ number of terms - last term
Last term = 2 and △ number of terms - first term
Number of items = (last first) / tolerance + 1
If the ratio of each term to its previous term is equal to the same non-zero constant from the second term, the sequence is called geometric progression. This constant is called the common ratio of the sequence. The common ratio is usually expressed by the letter Q (Q ≠ 0). Note: when q = 1, an is a constant sequence. (1) the general formula of the sequence is: an = A1 * q ^ (n-1)
General formula of equal ratio sequence
If the general term formula is changed to an = A1 / Q * q ^ n (n ∈ n *), when Q > 0, then an can be regarded as the function of independent variable n, and the point (n, an) is a group of isolated points on the curve y = A1 / Q * q ^ X. (2) summation formula: SN = Na1 (q = 1) Sn = A1 (1-Q ^ n) / (1-Q) = (a1-a1q ^ n) / (1-Q) = (a1-an * q) / (1-Q) = A1 / (1-Q) - A1 / (1-Q) * q ^ n (i.e. a-aq ^ n)
Summation formula of equal ratio sequence
(premise: Q ≠ 1) the relationship between any two terms am and an is an = am · Q ^ (n-m); when using the first n-phase sum of the equal ratio sequence, we must pay attention to whether the common ratio q is 1. (3) from the definition of the equal ratio sequence, the general term formula, the first N-term and the formula, we can deduce: A1 · an = A2 · an-1 = A3 · An-2 = =ak·an-k+1,k∈{1,2,… , n} (4) equal ratio middle term: AQ · AP = ar ^ 2, AR is AP, AQ equal ratio middle term An, then there are π 2N-1 = (an) 2N-1, π 2n + 1 = (an + 1) 2n + 1. In addition, an arithmetic sequence is formed by taking the same base number of each item of an arithmetic sequence which is positive. On the contrary, an arithmetic sequence is formed by taking any positive number C as the base and using the items of an arithmetic sequence as the index, We say: a positive term arithmetic sequence and arithmetic sequence are isomorphic, Every term (except the finite sequence and the last term) is the equal proportion middle term of its former term and the latter term. The equal proportion middle term formula: an / an-1 = an + 1 / an or (an-1) (an + 1) = an ^ 2 (5) infinitely decreasing equal proportion sequence items and formula: infinitely decreasing equal proportion sequence items and formula: infinite equal proportion sequence whose absolute value of common ratio is less than 1, The limit when n increases infinitely is called the sum of the items of the infinite equal ratio sequence. (6) the common ratio of the new equal ratio sequence composed of the equal ratio sequence: {an} is the equal ratio sequence with the common ratio of Q. if a = a1 + A2 + +an 　　B=an+1+…… +a2n 　　C=a2n+1+…… If a = a1 + A4 + A7 + +a3n-2 　　B=a2+a5+a8+…… +a3n-1 　　C=a3+a6+a9+…… +A 3N, a, B and C form a new equal ratio sequence, and the common ratio q = q is used to edit the properties of this paragraph
(1) If m, N, P, Q ∈ n *, and M + n = P + Q, then am * an = AP * AQ; (2) in the equal ratio sequence, the sum of each k term in turn is still equal ratio sequence. (3) "G is the equal ratio middle term of a and B", "G ^ 2 = AB (g ≠ 0)" (4) if {an} is equal ratio sequence, common ratio is Q1, {BN} is also equal ratio sequence, common ratio is Q2, then {A2N}, {a3n} It's an equal ratio sequence, the common ratio is Q1 ^ 2, Q1 ^ 3 (5) in an equal ratio sequence, the sum of continuous, equal length and equal interval segments is equal ratio. (6) if (an) is an equal ratio sequence and each item is positive, and the common ratio is Q, then (log a is the logarithm of an) is equal difference, The tolerance is the logarithm of log with a as the base Q. (7) the sum of the first n terms of the equal ratio sequence Sn = A1 (1-Q ^ n) / (1-Q) = A1 (Q ^ n-1) / (Q-1) = (a1q ^ n) / (Q-1) - A1 / (Q-1) (8) the sequence {an} is the equal ratio sequence, and an = PN + Q, then an + k = PN + k is also the equal ratio sequence. In the equal ratio sequence, the first term A1 and the common ratio Q are not zero. Note: in the above formula, a ^ n represents the nth power of A. (9) since the first term is A1, The formula of equal ratio sequence with common ratio Q can be written as an * q / A1 = q ^ n, and its exponential function y = a ^ x is closely related, so we can use the properties of exponential function to study equal ratio sequence. Edit the method of solving general term formula in this paragraph
(1) Undetermined coefficient method: given a (n + 1) = 2An + 3, A1 = 1, find an, construct the equal ratio sequence a (n + 1) + x = 2 (an + x) a (n + 1) = 2An + X, ∵ a (n + 1) = 2An + 3 ∵ x = 3, so (a (n + 1) + 3) / (an + 3) = 2 ∵ {an + 3} has the first term of 4 and the common ratio of 2, so an + 3 = A1 * q ^ (n-1) = 4 * 2 ^ (n-1), an = 2 ^ (n + 1) - 3

Solving process of quadratic equation with one variable (20-2x) (15-2x) = 246

(20-2x) (15-2x) = 246
Divide left and right by two
(10-x)(15-2x)=123
Open bracket
150-15x-20x+2x^2=123
2x^2-35x+27=0
You can't multiply by a cross
Use the general formula
have to
x=(35±√1009)/4

What are the examples in Deng Jiaxian's text that show the character's spiritual quality?
10 points will be added after the answer

Selfless dedication and love for the motherland

Let the integer part of &# 10004; 20 be x, and the decimal part be y. then, find the value of &# 178; + (y + 4) &# 178?

The integer part of 20 under the root sign is x, and the decimal part is y
Because √ 5 ≈ 2.236, then 2 √ 5 ≈ 4.472
So x = 4, y = 2 √ 5-4
Then the square of X + the square of (y + 4)
=4²+(2√5-4+4)²
=4²+(2√5)²
=16+20
=36

(x + 1 / 2) ^ 2 - (x + 1) (x-1) = 1 (solving equation)

﹙x＋1/2﹚²－﹙x＋1﹚﹙x－1﹚＝1
x²＋x＋1/4－x²＋1＝1
x＋1/4＝0
x＝﹣1/4.

The circumference of the bottom of a cube is 12 cm, and its volume is______ ．

12 △ 4 = 3 (CM); 3 × 3 × 3 = 27 (cm3); a: the volume of a cube is 27 cm3

Given ∈ (0, Π) and COS (a - Π / 6) = 3 / 5, find cosa

a∈(0,π)
cos(a-π/6)=3/5
sin(a-π/6)=4/5
cosa=cos[(a-π/6)+π/6]
=cos(a-π/6)*cosπ/6-sin(a-π/6)*sinπ/6
=3/5*1/2-4/5*√3/2
=3/10-4√3/10