A problem about binomial theorem It is known that the ratio of the coefficients of three consecutive terms in the expansion of (3 √ x + √ X / 1) to the nth power is 3:8:14. Find the constant term in the expansion. (please explain in detail)

Let three consecutive terms be K, K + 1 and K + 2. From the meaning of the problem, we can get that: C (n, k-1) / C (n, K) = K / (n-k + 1) = 3 / 8C (n, K) / C (n, K + 1) = (K + 1) / (n-k) = 8 / 14. From the above, we can get that: n = 10, k = 3. The general term of binomial expansion is m + 1 = C (10, m) x ^ [(10-m) / 3 + (- M / 2)] = C (10, m) x ^ [(20-5m) / 6]

The constant term of binomial theorem,
(3x ^ 3-1) (x ^ 2-1 / x) ^ 6, constant term. I didn't listen carefully before, but now I can't find it in the book

=3X^3*(x^2-1/x)^6-(x^2-1/x)^6
Constant term = 3x3 * C (6, I) * (x ^ 2) ^ I * (- 1 / x) ^ 6-i-c (6, J) * (x ^ 2) ^ J * (- 1 / x) ^ 6-j
2i+i-6=-3,2j=6-j,
i=1,j=2.
Constant term = 3 * C (6,1) * - 1) ^ 5-c (6,2) * - 1) ^ 4

What is the difference between the sum of the binomial coefficients and the sum of the coefficients in the expansion

The function f (x) = LNX + 3x-11 must have zero point ()
A. （0，1）B. （1，2）C. （2，3）D. （3，4）

When x = 1, 2, 3, 4, the function value y = - 8, ln2-5, ln3-2, 1 + ln4. According to the judgment theorem of zero point, we know that the zero point of function exists in (3, 4), so we choose D

The following parametric equations are transformed into ordinary equations and the curves they represent are explained
X = 3-2t, y = - 1-4t, t is the parameter
X = t + 1 / T, y = T-1 / T, t is the parameter

1: Because x = 3-2t, t = (3-x) / 2; and because y = - 1-4t, t = (- 1-y) / 4, so (3-x) / 2 = (- 1-y) / 4 is reduced to 2x-y-7 = 0, which represents a straight line
2: The two formulas are squared and subtracted to get x2-y2 = 4, which represents hyperbola

The application and examples of the method of factoring and complementing
5 points for one more example
Three at most
13891432275, your example is too simple.
Is there no other example?

a^+4a=(a^+4a+4)-4=(a+2)^-4=(a+2)^-2^=(a+2+2)(a+2-2)=a(a+4)a^+8a=(a^+8a+16)-16=(a+4)^-16=(a+4)^-4^=(a+4+4)(a+4-4)=a(a+8)a^+10a=(a^+10a+25)-25=(a+5)^-25=(a+5)^-5^=(a+5+5)(a+5-5)=a(a+10)

Given that there are three points on the plane which are not on the same line, then the parallelogram with these three points as the vertex has ()
A. 1
B. 2
C. 3
D. 4

C 3
Three points define a triangle
Only need to open a triangle side, the diagonal of the parallelogram line can be
There are three diagonal lines and three parallelogram lines

Calculate

2x＋3x =（2＋3）x =5x
Please accept

Given the vertex of the parabola y = (x + a) square + 2A square + 3a-5, find the value of the letter A on the coordinate axis and point out the position of the vertex

If the vertex is on the x-axis, the square of 2A + 3a-5 = 0, a = 1, or a = - 5 / 2, the vertex is (1,0), (- 5 / 2,0)
If the vertex is on the y-axis, a = 0, the vertex is (0, - 5)

Write a positive integer solution of quadratic equation 4x-7y = 3!

Just give x an integer value and calculate that y is also an integer
Let x = 6 and y = 3
Therefore, x = 6, y = 3 is a positive integer solution of the equation

A problem about binomial theorem It is known that the ratio of the coefficients of three consecutive terms in the expansion of (3 √ x + √ X / 1) to the nth power is 3:8:14. Find the constant term in the expansion. (please explain in detail)