How to solve the equation The letter equality is also reduced to equal to 0. If constant = 0, how to solve it is not an inequality

How to solve the equation The letter equality is also reduced to equal to 0. If constant = 0, how to solve it is not an inequality

The identity of letters is reduced to 0 * x = 0
Where X represents the algebraic formula composed of various letters, this equation is always true
If any problem about taking any value of an unknown number is solved, it will be transformed into an equation in this form,
For example, X * m = 0, no matter what value m takes, then if it is transformed into this form, the algebraic formula x = 0 can solve the problem
Other types of also take this form
Typing is not easy. If you have any questions, you can continue to ask,

1. F (x) = x ^ 3 + PX ^ 2 + QX image and X axis are tangent to a point other than the origin, and the minimum value is - 4. Find P, Q 2. F (x) = (1 + X / 1-x) e ^ (AX). For any x belonging to (0,1), there is always f (x) greater than 1. Find the range of A 3.lim (f(x+ Δ x)-f(x- Δ x))/2 Δ Is x the derivative of F (x) or 1 / 2F (x)?

1. Since the derivative is zero when the slope of the tangent equation passing through the tangent point is zero, and the derivative at the extreme point is also zero, the two roots X1 and X2 of F '(x) = 3x ^ 2 + 2px + q = 0 (1 -- 1) satisfy respectively, f (x1) = 0; F (x2) = - 4 combined with (1 -- 1) to eliminate the third power, P / 3 (x1) ^ 2 + 2q / 3 (x1) = 0. Since x1 ≠ 0, X1 = - 2q /

For a cylindrical boiler with a volume of V, the price per unit area of two bottom materials is a yuan, and the price per unit area of side materials is B yuan. What is the ratio of bottom diameter to height of the boiler, the cost is the lowest?

The bottom diameter of the cylindrical container is D and the height is h
Then volume v = Πd ^ 2H / 4
The cost is p = 2 Π d ^ 2A / 4 + Π DHB = Π d ^ 2A / 2 + 4vb / d
P'= dP/dD =∏Da -4Vb/(D^2)
Let p '= 0
The solution is: D = cubic root sign 4vb / Πa, H = 4V / Πd ^ 2
At this time, D / h = Π d ^ 3 / 4V = B / A, so the cost is the most economical when the ratio of diameter to height is B / A

What does this second derivative problem mean? The title is as follows: F (X-Y, Y / x) = x ^ 2-y ^ 2, F "the subscript is XX. How and what is the problem? Can you explain it in detail? I just don't understand what F "there are two X's below" means If it is to find the second derivative of X, shouldn't it be expressed by F "(x)?

F "subscript XX means: first find the partial derivative of the given binary compound function to x, and then find the partial derivative of the obtained result to x, that is, find the second-order partial derivative of the given binary function to the independent variable x

It is known that the definition domain of function FX is r, where f (x) + F (y) = f (x + y). When x < 0, f (x) > 0 is always true It is proved that y = f (x) is an odd function

F (0) + F (0) = f (0). So f (0) = 0
F (x) + F (- x) = f (0) = 0. So f (x) = - f (- x)
So it's an odd function. I don't know what your f (x) > 0 is when x < 0

(1) It is known that the domain of the function y = f (x) is r, and when x ∈ R, f (M + x) = f (M-X) is constant. It is proved that the image of y = f (x) is symmetrical about the straight line x = M; (2) If the axis of symmetry of the image of function y = log2 | AX-1 | is x = 2, find the value of non-zero real number a

(1) It is proved that if P (s, t) is any point of y = f (x) image, then t = f (s),
If the symmetry point of point P with respect to x = m is p ', then p' (2m-s, t),
From the known f (M + x) = f (M-X), f (2m-s) = f (M + (M-S)) = f (M - (M-S)) = f (s) = t,
That is, p 'is on the image of y = f (x),
The image of y = f (x) is symmetrical about the straight line x = m;
(2) ∵ the axis of symmetry of the image of the function y = log2|ax-1|is x = 2,
‡ log2|a (2 + x) - 1| = log2|a (2-x) - 1|is established,
That is | a (2 + x) - 1 | = | a (2-x) - 1 |,
That is, | ax + (2a-1) | = | ax + (2a-1) | Heng is established,
∵ a ≠ 0, ∵ 2a-1 = 0, that is, a = 1
2．