Given the position of the real number a on the number axis as shown in the figure (a is in the middle of 0 and - 1), the result of simplifying the absolute value of 1-A + the square of root a is? A.1 B.-1 C.1-2a D.2a-1 Seek analysis

Given the position of the real number a on the number axis as shown in the figure (a is in the middle of 0 and - 1), the result of simplifying the absolute value of 1-A + the square of root a is? A.1 B.-1 C.1-2a D.2a-1 Seek analysis

The absolute value of 1-A + the square of root a = 1 + A-A = 1, so choose a

The position of real numbers a, B, C on the number axis is shown in the figure, and the absolute value a = absolute value B. simplify the square of the over sign of absolute value a plus absolute value a plus b-radical c-z A < 0, C < 0, b > 0, the absolute value of a = the absolute value of B, C < a

When C is on the left of a, = - A + 0 - (A-C) + 2 (- C) = 2a-c
When C is to the right of a, = - A + 0 - (C-A) + 2 (- C) = 3C
If C < A, then = - A + 0 - (A-C) + 2 (- C) = 2a-c

If the square of (1 + m) + the absolute value of n-1 = 0, then 2n to the 2006 Power - 3m to the power of 2007=

The square of (1 + m) + the absolute value of n-1 = 0
1+m=0,n-1=0
m=-1,n=1
2n to the power of 2006 - 3m to the power of 2007
=2×1-3×(-1)
=2+3
=5

The square of 15x and the nth power of y can be combined into one term. What is the absolute value of minus 2m plus N plus m minus 3N

The square of 15x and the power of M of minus 2 / 9 x and the power of y can be combined into one term, ﹥ M = 2; n = 0; then the absolute value of minus 2m plus N plus m minus 3N = 4 + 2 = 6

It is known that 3M power = a, 3N power = B, and a, B denote 3M + n power and 3

3M + nth power
=3M power × 3N power
=ab

The third power of M is a positive number, and the fifth power of n is a negative number, I'm - 3m-3n-6. What's wrong?

Because m ^ 3 > 0 (any power of a positive number is a positive number)
∴m＞0
Because n ^ 5

If M + 4 = n n + 4 and m ≠ n, find 3M + 3N

If M + 4 │ = | n + 4 | and m ≠ n, then
M＋4=-（N＋4）=-N-4
M+N=-8
3M＋3N=3（M+N）=-24

How to get - 3M + 4 = - 3N + 4 from M = n

Multiply both sides by - 3
The result is - 3M = - 3N
Add four on both sides
-3m+4=-3n+4

(m-n)(3m+n)^2+(m+3n)^2(n-m) Factorization factor

solution
(m-n)(3m+n)²+(m+3n)²(n-m)
=(m-n)(3m+n)²-(m+3n)²(m-n)
=(m-n)[(3m+n)²-(m+3n)²]
=(m-n)[(3m+n)+(m+3n)][(3m+n)-(m+3n)]
=(m-n)(4m+4n)(2m-2n)
=8(m-n)(m+n)(m-n)
=8(m-n)²(m+n)

If m, n belong to R, compare the size of m ^ 4-m ^ 3N and n ^ 3m-n ^ 4

(1) when m = n, X-Y = 0, that is: m ^ 4-m ^ 3 * n = n ^ 3 * n ^ 3 * n ^ 3 * m + n ^ 4 = m (m ^ 3-N ^ 3) - n (m ^ 3-N ^ 3) = (m-n) (M ^ 3-N ^ 3) (1) when m = n, X-Y = 0, that is: m ^ 4-m ^ 3 * n = n ^ 3 * M-N ^ 4 (2) when m ≠ n, X-Y > 0 means: m ^ 4-m ^ 3 * n > n ^ 3 * M-N ^ 4 (2) when m ≠ n, X-Y > 0, that is: m ^ 4-m ^ 4-m ^ 3 * n > n ^ 3 * n ^ 3 * M-3 * M-N ^ 3 * in conclusion, m ^ 4-m ^ 3 * n ≥ n ^ 3 * M-N ^ 4