Given that the absolute value of M is equal to 4, and M > 0, a = (- 1) to the power of M, a and B are opposite numbers to each other, B and C are reciprocal numbers to each other, find 2 of the power of M - (B-C) of AB + B Given that the absolute value of M is equal to 4, and M > 0, a = (- 1) to the power of M, a and B are opposite to each other, B and C are reciprocal to each other, find the value of AB + B to the power of M - (B-C) to the power of 2008

Given that the absolute value of M is equal to 4, and M > 0, a = (- 1) to the power of M, a and B are opposite numbers to each other, B and C are reciprocal numbers to each other, find 2 of the power of M - (B-C) of AB + B Given that the absolute value of M is equal to 4, and M > 0, a = (- 1) to the power of M, a and B are opposite to each other, B and C are reciprocal to each other, find the value of AB + B to the power of M - (B-C) to the power of 2008

The absolute value of M is equal to 4, and m ＞ 0, we can know that M = 4; the m power of a = (- 1), because m is even, the even power of - 1 is 1, so a = 1; a and B are opposite numbers, so B = - 1; B and C are reciprocal, C = - 1ab + b m power - (B-C) 2 power = (- 1) * 1 + (- 1) 4 power - (- 1 + 1) 2 power = 0-0 = 0
m=4, a=1, b=-1,c=-1
(ab+b)^4 - (b-c)^2008 = 16 - 0 = 16
If it is
ab + b^4 - (b-c)^2008 = 0
It's all zero
The equation 2x-6 = 4K and two-thirds of x-k = k-3x have the same root, so we can find the value of K
From 2x-6 = 4K to x = 2K + 3, from X / 2-k = k-3x to x = 4K / 7
So 2K + 3 = 4K / 7
14k+21=4k
10k=-21
k=-21/10
It is known that a and B are opposite to each other, C and D are reciprocal to each other, and the absolute value of M is equal to 3. Find the value of 3 (a + b) - 2CD + m to the fourth power
therefore
a+b=0,cd=1,|m|=3
3 (a + b) quartic-2cd + M
=0-2+m
=m-2
m=±3
therefore
The original formula
=3-2=1
perhaps
=-3-2=-5
A and B are opposite numbers, a + B = 0
C and D are reciprocal, CD = 1
The absolute value of M is 3, M = 3 or M = - 3
When m = 3, the fourth power of 3 (a + b) - 2CD + M = 3x0 - 2x1 + 3 = 1
When m = - 3, the fourth power of 3 (a + b) - 2CD + M = 3x0 is - 2x1-3 = - 5
The solution of the equation 2x-3 = 4K and x-k △ 2 = k-3x of X are the same
2x-3=4k.①
x-k/2=k-3x.②
From ②, 2x = 3K / 4. ③ is substituted into ①
3k/4-3=4k
k= -12/13
It is known that a and B are opposite to each other, C and D are reciprocal to each other, and the absolute value of M is 3. Find the absolute value of - 2CD + m of A-1 + B, which is the fourth of the formula
The absolute value of M is 3
Then a + B = 0, CD = 1, M = ± 3
The absolute value of A-1 + B is - 2CD + M
=1/4-2+m
= -7/4+m
When m = 3, the above formula = - 7 / 4 + 3 = 5 / 4
When m = - 3, the above formula = - 7 / 4-3 = - 19 / 4
The absolute value of A-1 + B is - 2CD + M
=1/4-2+m
=m-7/4;
=5 / 4 or - 19 / 4;
Given that the solution of the equation 3x-1 = x + 6 is 2 larger than that of the equation 2x-4k = x + 3, find the value of K
3x-1=x+6
3x-x=6+1
2x=7
x=7/2
2x-4k=x+3
x=3+4k
7/2 - 3 -4k = 2
-4k=5- 7/2
-4k=3/2
k=-3/8
-3/8
k=1/8
If 3x-1 = x + 6, then 2x = 7, x = 7 / 2
2 * 7 / 2-4k = 7 / 2 + 3, then k = 1 / 8
3x-1=x+6
2x=7
x=7/2
2x-4k=x+3
x=4k+3
Xie Da 2,
So 7 / 2 = 4K + 3 + 2
4k=7/2-5=-3/2
k=-7/8
When x = - 2, y = - 3, find the value of the algebraic formula | Y-X | - 2 | XY |
The original formula = | - 3 + 2 | - 2 | (- 3) | = 1-12 = - 11
－11
Find the equation 4k-3x / K + 2 = 2x about X when k is a value
The solutions are 1 positive and 2 negative
Obviously, K ≠ 0, because it appears on the denominator
So the original equation can be changed into:
4k²－3x＋2k＝2kx
That is, (2k + 3) x = 4K & # 178; + 2K
If 2K + 3 = 0, then k = - 3 / 2, so 4K & # 178; + 2K = 6, the equation is reduced to 0 x = 6, and there is no solution
So 2K + 3 ≠ 0, that is k ≠ - 3 / 2
The solution of this equation is x = (4K & # 178; + 2K) / (2k + 3)
Of course, we can also write x = 2K (2k + 1) / (2k + 3)
【1】 If the solution of the equation is positive
That is to say, x = 2K (2k + 1) / (2k + 3) > 0
That is, (2k + 3) and 2K (2k + 1) have the same sign
》When 2K + 3 ＞ 0, that is, K ＞ - 3 / 2, 2K (2k + 1) ＞ 0, which means that 2k and (2k + 1) have the same sign
》》If 2K > 0, that is, k > 0, it is obvious that 2K + 1 > 0 holds
》》If 2K ＜ 0, that is, K ＜ 0, the solution 2K + 1 ＜ 0 is k ＜ - 1 / 2
》》So the solution set of 2K (2k + 1) > 0 is k ＜ - 1 / 2 or K ＞ 0
》So the range of K is - 3 / 2 ＜ K ＜ - 1 / 2 or K ＞ 0
》When 2K + 3 ＜ 0, i.e. K ＜ - 3 / 2, 2K (2k + 1) ＜ 0, which shows that 2K is different from (2k + 1)
》》If 2K > 0, that is k > 0, it is obvious that 2K + 1 < 0 will never hold
》》If 2K ＜ 0, that is, K ＜ 0, the solution 2K + 1 ＞ 0 gives K ＞ - 1 / 2
》》So the solution set of 2K (2k + 1) < 0 is - 1 / 2 < K < 0
》Therefore, the real number K does not exist because there is no intersection between K ＜ - 3 / 2 and - 1 / 2 ＜ K ＜ 0
So when - 3 / 2 ＜ K ＜ - 1 / 2 or K ＞ 0, the solution of the equation is positive
【2】
The process is the same as [1]. It can be concluded that when k ＜ - 3 / 2 or - 1 / 2 ＜ K ＜ 0, the solution of the equation is negative
Note: if you have learned the solution of higher-order inequality, after finding out x = 2K (2k + 1) / (2k + 3), you can,
When x ＞ 0, it can be transformed into 2K (2k + 1) (2k + 3) ＞ 0
If M and N are opposite to each other and are not zero, and X and y are reciprocal to each other, find XY (M + n) - M △ n + 2XY
m. If n is opposite to each other and not zero, then M + n = 0, n = - M; if x and y are reciprocal to each other, then xy = 1
So XY (M + n) - M △ n + 2XY = 1 × 0-m △ (- M) + 2 × 1 = 1 + 2 = 3
It is known that the univariate quadratic equation x-4x + k = 0 and 2x-3x + k = 0 have the same root, so we can find the value of K
Let the root of x ^ 2-4x + k = 0 be x, and the root of a 2x ^ 2-3x + k = 0 be x, B. according to Weida's theorem, if x + a = 4, X * a = k, then (4-x) * x = k, x + B = 3 / 2, X * b = K / 2, then (3 / 2-x) * x = K / 2, so (4-x) * x = 2 * (3 / 2-x) * x x ≠ 0 [when x = 0, the two equations become k = 0, there are innumerable solutions, which is not satisfactory] so 4-x = 2 * (3 / 2-x) can get x = - 1, so a = 5K = x * a = - 5