A simple equation of one variable with brackets is compiled, and its solution is x = - 1 / 2

A simple equation of one variable with brackets is compiled, and its solution is x = - 1 / 2

For example, (1) 2 (x-1) = 1 + 8x (2) x / 3 + (1-x) / 2 = 7 / 12

Implicit function derivation example, example 15,16,

You need to know the derivation rule of product function, that is, the derivation rule of (f * g) '= f'g + FG' composite function, that is, f (g (x)) '= f' (g (x)) g '(x). You will understand these two formulas.

Factorization of x ^ 3 + 8y ^ 3

x^3+8y^3
=(x+2y)(x^2-2xy+4y^2)

If the square root of X + 2 + the absolute value of Y-1 = 0, what is the relationship between P (x, y) and Q (2x + 2, Y-2)?

The sum of the two nonnegative terms = 0, and the two nonnegative terms = 0 respectively
x+2=0 x=-2
y-1=0 y=1
2x+2=2×(-2)+2=-2
y-2=1-2=-1
Point P coordinates (- 2,1), point Q coordinates (- 2, - 1), point P and point q are symmetric about X axis

If f (x) is a quadratic function, f (0) = 3, and f (2x) - f (x + 1) = 3x ^ 2 + 5x-8, find f (x)

Let f (x) = ax ^ 2 + BX + 3,
Then f (2x) - f (x + 1) = a (2x) ^ 2 + B (2x) + 3-A (x + 1) ^ 2-B (x + 1) - 3 = 3ax ^ 2 + (2b-2a-b) x + (- a-b)
So 3A = 3, 2b-2a-2b = 5, - A-B = - 8,
The solution is a = 1, B = 7
So, f (x) = x ^ 2 + 7x + 3

In the linear function y = (2m-6) x + 5, y decreases with the increase of X, then the value range of M is

2m-6

The sum of each digit of a three digit number is equal to 12. His one digit number is 2 less than ten digit number. If his hundred digit number is interchanged with each digit number
The result is 99% smaller than the original
Seeking process

abc-cba=99=(a-c)*100+(c-a)=(a-c)*(100-1)=(a-c)*99
So a-c = 1
a+b+c=12
c=b-2
So C = 3
a=4
b=5
The original number is ABC, which is 453

24a square B cube C (x + Y-Z) - 18a cube BC square (z-y-x) - 36abc (x-z + y)

24a²b³c(x+y-z)-18a³bc²（z-y-x)-36abc(x-z+y)
　　=24a²b³c(x+y-z)+18a³bc²(x+y-z)-36abc(x+y-z)
　　=6abc(x+y-z)(4ab²+3a²c-6)

2.8 times 4-5x = 5.8 to solve the equation

2.8×4-5x=5.8
11.2-5x=5.8
5x=5.4
x=1.08

Given that the ellipse X / 9 + Y / 4 = 1 and the point d [2,1], through the point D, any straight line is drawn to intersect the ellipse at two points a and B, and the trajectory equation of the midpoint m of the line AB is obtained?

The AB equation is: y = K (x-2-x-2) + 1, then: x ^ 2 / 9 / 9 + [K (X-2) + [K (X-2) + (1] ^ 2 / 4 = 1 (4 + 9K ^ 2) as the AB equation is: the AB equation is: y = K (x-2-2 (x-2-2-2-2) + 1 (x ^ 2 / 2 / 9 (4 + 9K ^ 2) as follows: x ^ 2 / 2 / 9 / 9 [2 / 9 [K (4 + 9K ^ 9K ^ 2) as the (4 + 9K ^ 9K ^ 2) is the (4 + 9K ^ 9K ^ 2) as (4 + 9K ^ 9K ^ 9K ^ 2) as (4 + 9K ^ 2) as the AB point in the AB, let the AB point in the AB equation is: X, then: let the AB equation is: x = x = x, then: x = x = x = x = x = x = x = x, k-1) / (4 + 9K ^ 2) y = (Y1 + Y2) / 2 = - 4 (2k-1) / (4 + 9K ^ 2) so, X = - KY substitute: k = - X / Y into: y = K (X-2) + 1 to get: y = - x (X-2) / y + 1 y ^ 2-y + X (X-2) = 0. This is the trajectory equation of point m in line ab