It is known that (M & # 178; - 1) x & # 178; + (M + 1) x + 1 = 0 is a linear equation of one variable with respect to x, and the value of M & # 178; - 2m + 1 is obtained 2 if (M-3) times the absolute value of 2 times m of x minus 5 to the power of - 4m = 0 is a one variable linear equation about X, find the value of M & # 178; - 2m + 1,

It is known that (M & # 178; - 1) x & # 178; + (M + 1) x + 1 = 0 is a linear equation of one variable with respect to x, and the value of M & # 178; - 2m + 1 is obtained 2 if (M-3) times the absolute value of 2 times m of x minus 5 to the power of - 4m = 0 is a one variable linear equation about X, find the value of M & # 178; - 2m + 1,

1 according to the meaning of the problem: m ^ 2-1 = 0 and M + 1 = 0, the solution is m = 1  m ^ 2-2m + 1 = 0
It is known that (M & # 178; - 1) x & # 178; - (m-1) x + 8 = 0 is a linear equation of one variable with respect to X,
Its solution is n. try to find the solution of the equation about y, m times the absolute value of y = n
This problem is about the calculation and exponent of the equation, ∵ (M & # 178; - 1) x & # 178; - (m-1) x + 8 = 0 is the univariate linear equation of X, the coefficient of x = 0, the coefficient of X ≠ 0, that is, M & # 178; - 1 = 0, and M-1 ≠ 0 ≠ M = - 1, substituting M = - 1 into (M & # 178; - 1) x & # 178; - (m-1) x + 8 = 0, the equation 2x + 8 = 0, x = - 4, n = x =
(M & # 178; - 1) x & # 178; - (m-1) x + 8 = 0 is a linear equation of one variable with respect to X,
m²-1=0
m-1≠0
So m = - 1
The solution is x = - 4
That is, n = - 4
So - | y | = - 4
So y = - 4 or 4
The original equation is a linear equation about X, so m ^ 2 = 1, that is m = 1 or - 1. Considering that - (m-1) x + 8 = 0 is a linear equation about X, we can only take M = - 1;
When m = - 1, the linear equation is 2x + 8 = 0, so x = - 4 = n;
-Iyi = - 4, that is, iyi = 4, so y = - 4 or y = 4
How to solve this system of Fractional Inequalities
It is known that a is less than 0
2 / A is greater than - 1, 1 / A is less than 1
∵a＜0
In 2 / a ≥ - 1, 2 ≤ - A is obtained by removing the denominator,
∴a≥-2
From 1 / a ≤ 1 to denominator 1 ≥ a
In conclusion - 2 ≤ a < 0
1, a is less than 0
2, a is less than or equal to - 2
3, a is greater than or equal to 1
To sum up, the original inequality has no solution
Finding the remainder of 243 divided by 7 to the power of 2001
Another congruence problem
243÷7=34…… Five
To find the remainder of 243 divided by 7 to the power of 2001 is to find the remainder of 5 divided by 7 to the power of 2001
5÷7=0…… 5 5×5÷7=3…… 4 5×5×5÷7=17…… Six
5×5×5×5÷7=89…… 2 5×5×5×5×5÷7=446…… Three
5×5×5×5×5×5÷7=2232…… One
5×5×5×5×5×5×5÷7=11160…… Five
…………
The cycle is six
2001÷6=333…… Three
The remainder of the third group is 6
So the remainder of 243 divided by 7 to the power of 2001 is 6
It's 2. Look at my first one
6. Cycle of 666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666
It's about six
How to solve Fractional Inequality
First, the right side of the inequality is moved to the left side, and the coefficients of X are changed to positive numbers,
When the numerator and denominator of the contact fraction are 0, the value of X is calculated according to the value less than the middle of the clip and greater than the two sides of the fraction; the complex value can be expressed by drawing the number axis
(x + y minus z) 3N power multiplication (y minus Z plus x) 2n power multiplication (x minus Z plus y) 5N power n is a natural number
(x + y minus z) 3N times (y minus Z plus x) 2n times (x minus Z plus y) 5N
=(x + Y-Z) 3N power multiplied by (x + Y-Z) 2n power * (x + Y-Z) 5N power
=(x + Y-Z) 10N power
The needle and thread method for solving higher order inequality
Using derivative to find the monotonicity and interval of F (x) = x ^ 3 + x ^ 2-x, I find that 3x ^ 2 + 2x-1 > 0, 3x ^ 2 + 2x-1 < 0 (x + 1) · (3x-1) > 0 (x + 1) · (3x-1) < 0
We have found that the zeros of the derivative function are - 1 and 1 / 3
Moreover, the derivative is a quadratic polynomial, and the coefficient of the highest degree term is positive
So draw - 1 and 1 / 3 on the real axis, draw a line from the top right to the left, because these two zeros are single, so draw down through 1 / 3, then draw up through - 1, and get a line
When X1 / 3, the line is on top, so the derivative is positive and the function is increasing
When - 1
The 3N power of (x + Y-Z) multiplied by the 2n power of (z-x-y) multiplied by the 5N power of (x-z-y)
Original formula = (x + Y-Z) ^ 3N (x + Y-Z) ^ 2n (X-Y-Z) ^ 5N
=(x+y-z)^5n(x-y-z)^5n
=[（x-z)^2-y^2]^5n
^The superscript is on the back~
(x+y-z)^3n*(z-x-y)^2n*(x-z-y)^5n
=（z-x-y）^2n
=(x+y-z)^2n
On the problem of solving inequality - pin through method
If log2x (1 + log2x) (1-log2x) > 0 (1), the negative sign is raised
log2x（1+log2x)（log2x-1)
The coefficients of the unknowns must be all positive by the rule of puncturing
Therefore, needling is not allowed
It has to be transformed into 2
Odd up even down
If the solution of a function is - 102, then the curve will go through 2 from right to left, top to bottom, go through 0 from below, and then go through - 1 from above. This is what the image looks like. Note that if the solutions are the same, then you will go through this point instead of going through it
On the "pinprick method" to solve multiple inequalities, it is to draw a curve from right to left through the end point on the number axis, first decompose the factor and then find each root, also known as "pinprick". After adjusting each factor to lower row, pay attention to the first of each factor
3N power of X - 2n power of X + 1 = 0, find 5N power of X + n power of X + 2013
∵ 3N power of X - 2n power of X + 1 = 0 ∵ 3N power of x = 2n power of X - 1 ∵ 5N power of X + n power of X + 2013 = 3N power of X * 2n power of X + n power of X + 2013 = (2n power of X - 1) * 2n power of X + n power of X + 2013 = 4N power of X - 2n power of X + n power of X + 2013 = 3N power of X * n power of X