It is known that the expanded result of (X & # 178; + MX + n) (X & # 178; - 3x + 1) does not contain X & # 178; and X & # 179;. Find the value of M and n

It is known that the expanded result of (X & # 178; + MX + n) (X & # 178; - 3x + 1) does not contain X & # 178; and X & # 179;. Find the value of M and n

=X^4+(M-3)X^3+(N-3M+1)X^2+(M-3N)X+N M=3 N=8

If the expansion of (X & # 178; + MX + 8) (X & # 178; - 3x + n) does not contain X & # 178; and X & # 179; terms, try to find the value of M.N

Original formula = X4 + X3 (- 3 + m) + X2 (n-3m + 8) + X (mn-24) + 8N
So - 3 + M = 0
n-3m+8=0
So m = 3
n=1

There are two functions f (x) = asin (KX + π / 3), G (x) = btan (KX - π / 3) (k > 0), and their periodic sum is known to be 3 π / 2,
And f (π / 2) = g (π / 2), f (π / 4) = - √ 3G (π / 4) + 1

F (x) = asin (KX + π / 3), G (x) = btan (KX - π / 3) (k > 0). We know that the sum of their periods is 2 π / K + π / k = 3 π / 2, k = 2. Furthermore, f (π / 2) = g (π / 2), f (π / 4) = - √ 3G (π / 4) + 1, - A (√ 3) / 2 = - B √ 3, a / 2 = - √ 3 * B (1 - √ 3) / (1 + √ 3) + 1

[about mathematics] is the equation with absolute value sign a linear equation of one variable?
For example, IXI + 3 = 9 and so on

Yes, it's just a classified discussion
For example, x = 9-6
X = 3
x1=3,x2=-3

On the parity of inverse function
1. Is the parity of the original function and the inverse function the same
2. Is it true that only monotone functions have parity

In order to solve this problem, we must grasp the definition. The definition of inverse function is as follows: generally, if x and Y correspond to some corresponding relation f (x), y = f (x), then the inverse function of y = f (x) is y = f '(x). The condition of existence of inverse function is that the original function must be "one-to-one correspondence", just like shooting a target: one person only has

What is the derivative of Ln (1 + 1 / x)?
What is the derivative of Ln (1 + 1 / x)?

See figure

Let a > 0, f = e ^ X / A + A / e ^ X be the even function on R. ① find the value of a; ② prove that f is an increasing function on R
I don't know how to start

(1) F (x) = f (- x) constant holds (e ^ x) / A + A / (e ^ x) = 1 / (AE ^ x) + AE ^ x (A-1 / a) (e ^ X-1 / e ^ x) = 0 constant holds, so a = 1 / A, a > 0, so a = 1 (2) f (x) = e ^ x + 1 / e ^ x derivative, f '(x) = e ^ X-1 / e ^ x = (e ^ 2x-1) / e ^ x x > 0, e ^ 2x > 1, e ^ x > 0, so f is an increasing function. If you haven't learned, you can use the definition method to set X1 and X2 quickly

Let a and B be orthogonal matrices of order n, and prove that the adjoint matrix A * of a is also orthogonal

AA^T=A^TA=E,A^(-1)=A^T
|A|^2=1,
|A|=1.-1
A * = |a ^ (- 1) = a ^ t or - A ^ t
When a * = a ^ t,
A*(A*)^T=A^T(A^T)^T=A^TA=E
When a * = - A ^ t,
A*(A*)^T=(-A^T)(-A*)^T=(-A^T)(-A)=A^TA=E
So it is proved that a * is also an orthogonal matrix

When the subject clause is guided by what, what should be the singular and plural of the predicate in the subject clause?
It seems that sometimes the predicate is singular. How can we distinguish it?

The predicate of what leading clause is singular~
If it's "what clause and what clause" then use the plural~

How to simplify - x < 5 in mathematics?

x>-5.