![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given that a and B are real numbers, and the root sign a + 1 + root sign 1-B = 0, what is the value of a power 2011-b power 2012
The sum of the two arithmetical square roots is 0, and the two arithmetical square roots are 0 respectively
a+1=0 a=-1
1-b=0 b=1
a^2011-b^2012
=(-1)^2011-1^2012
=-1-1
=-2
(- 1) 2012 power - absolute value of root number 18 + 2cos45 ° + - root 4 3 (root 3 - π) 0 power - root 5 / root 20 root sign 15 + (- 1) 2011 (- 1) the absolute value of Radix 18 + 2cos45 ° + - Radix 4 3 (root 3 - π) 0 power - 5 / 5 root sign 20 - root 15 + (- 1) 2011 power (π - 2010) 0 power + (sin 60 °) - 1 power - Tan 30 ° - the absolute value of root 3 + root 8 (there is a 3 at the top right of the root)
3×1-(√20/√5-√15/√5)+(-1)
=3-(√4-√3)-1
=3-2+√3-1
=√3
How can we prove that the integral of the square power of - t of E is equal to the root PI in the range of real numbers
∫e^(-t^2)dt=√π,(-∞,+∞)
prove:
Let I = ∫ e ^ (- x ^ 2) DX, (- R, R)
Then I = ∫ e ^ (- y ^ 2) dy, (- R, R)
I^2=∫e^(-x^2)dx∫e^(-y^2)dy,x∈(-R,R),y∈(-R,R)
I ^ 2 = ∫ e ^ [- (x ^ 2 + y ^ 2)] DXDY, X ∈ (- R, R), y ∈ (- R, R)
Transform coordinate system, convert rectangular coordinate system into polar coordinate system
ρ^2=x^2+y^2
θ=arctany/x
Then ∫ e ^ (- ρ '^ 2) ρ'd ρ'd θ < I ^ 2 ∫ e ^ (- ρ ^ 2) ρ D ρ D θ
ρ'∈[0,R),θ∈[0,2π];ρ∈[0,√2R),θ∈[0,2π]
And ∫ e ^ (- ρ ^ 2) ρ'd ρ'd θ, ρ '∈ [0, R), θ∈ [0,2 π]
=π∫e^(-ρ'^2)dρ'^2,ρ'∈[0,R)
=π[1-e^(-R^2)]
∫∫e^(-ρ^2)ρdρdθ,ρ∈[0,√2R),θ∈[0,2π]
=π∫e^(-ρ^2)dρ^2,ρ∈[0,√2R)
=π[1-e^(-2R^2)]
So π [1-e ^ (- R ^ 2)] < I ^ 2 < π [1-e ^ (- 2R ^ 2)]
Because Lim π [1-e ^ (- R ^ 2)] = Lim π [1-e ^ (- R ^ 2)] = π, I = ∫ e ^ (- T ^ 2) DT, (- ∞, + ∞). R → + ∞
So ∫ e ^ (- T ^ 2) DT = √π, (- ∞, + ∞)
If the real number m satisfies the square minus the root sign of M, plus one equals zero, then the fourth power of M minus the negative fourth power of M is equal to? My third day in junior high school That symbol doesn't understand ^ what's this
Grade 4? M ^ 4 = (root 10 1) ^ 2 = 11 2 * root 10 m ^ (- 4) = 1 / 11 2 * root 10 = 11-2 * root 10 / ((11 2 * root 10) (11-2 * root 10)) = 11 2 * root 10 / 81 M ^ 4
Real numbers a and B satisfy that the sum of the roots A-2 and B-3 is equal to 0. Find the fourth power of a + the square root of B 2
Because: A and B satisfy the sum of radical A-2 and radical B-3 equal to 0
And a and B are real numbers
Then: root A-2 = 0, radical B-3 = 0
That is, a = 2, B = 3
Brought to the 4 of a + the square of B = 25
Then the square root is 5
Given that m, n are real numbers, and the root sign 2m-3 + | 2n - cubic root - 8 | = 0, then 1-m quadratic - n2004 power
Because √ (2m-3) + | 2n - 3 √ (- 8) | = 0,2n - 3 √ (- 8) = 2n + 2
So 2m-3 = 0 and 2n + 2 = 0
m=3/2,n=-1
therefore
1-m? - n ^ 2004 ^ denotes the power
=1-(3/2)²-(-1)^2004
=1-9/4-1
=-9/4
The result is nine quarters of minus
If the real number m satisfies M 2 minus m × Radix 10 + 1 = 0, then M quartic + 1 / M quartic
From M 2 - √ 10 m + 1 = 0, we can get √ 10 m = m ~ 2-2 m ~ 2 + 1, simplify m ^ 4 = 8m ~ 2 - 1, then we can get m ^ 8 = 64M ^ 4-16m ~ 2 + 1, then m ^ 4 + 1 / m ^ 4 = (m ^ 8 + 1) / m ^ 4 = (496m
If the real number a satisfies a + the square of root a + the cubic root of a = 0, find the value of A
The square of root a = | a|
The cubic root a to the power of a = a
So 2A + |a| = 0
If a > = 0, | a | = a
Then 3A = 0
A=0
If a
We know that the square of the root (2x-y) is 1, and the cubic root of the cube (x-2y) is = - 1, Given the root sign (2x-y) 2 = 1 and the cube root (x-2y) 3 = - 1, find the value of 3x + y According to the meaning of the square root of arithmetic, from the root sign (2x-y) 2 = 1, we get (2x-y) 2 = 1, then we get 2x-y = 1 According to the UJN meaning of cube root, cube root (x-2y) 3 = - 1, x-2y = - 1 The solution of {2x-y = 1 is obtained from ① and ②, and {x = 1 is obtained x-2y=-1 y=1 Substituting X and Y into 3x + y, we get 3x + y = 4 What is the wrong step in the process of solving the problem? What does it neglect? Try to analyze and write the correct solution process
The first step is wrong. 2x-y = 1 can also be equal to - 1
X-2Y=-1
x=2y-1
4y-2-y = 1 or - 1
Y = 1 or 1 / 3
When y = 1, x = 1
When y = 1 / 3, x = - 1 / 3
3x + y = 4 or - 2 / 3
It is known that a = x − y x + y + 3 Is the arithmetic square root of X + y + 3, B = x − 2Y + 3 x + 2Y Is the cube root of X + 2Y. Try to find the cube root of b-a
From the meaning of the title,
x−y＝2
x−2y+3＝3 ，
The solution is as follows:
x＝4
y＝2 ，
Then a = 3, B = 2,
B-A = - 1, and the cube root of - 1 is: - 1
RELATED INFORMATIONS
- 1. It is known that the third power of (x + 1) is 8 and the square root of root y is 2. Find the square root and cube root of X + y
- 2. If x < 0, it will be very fast to simplify the square of root X - the third power of root X!
- 3. 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
- 4. Rational number M. n is opposite to each other X. y is reciprocal to each other. The absolute value of Z is equal to 7. Find the value of 3M + 3N + 5Y + Z. who can help me
- 5. Whether there is a positive integer n, is 1 / (root sign 3N + 2) is a rational number If so, give a value of N. if not, give the reason It can be said that the radical sign 3N + 2 = a 3n+2=a^2 n=(a^2-2)/3 And then what do you say?
- 6. Simplify root sign [16 + 2 (1 + root 5) (1 + 2 and root 3)]
- 7. Calculate 3 / 3 root sign 6 × root 2
- 8. It is known that the fractional part of 5 + radical 7 is a, the integer part is m, the decimal part of 5-radical 7 is B, and the integer part is n. find the value of (a + b) ^ 2012 Mn
- 9. Given the real number a.b.c.d.m, if a and B are opposite to each other, C.D are reciprocal, and the absolute value of M is 2, find the square root of a + B divided into the square root of M + m and the square root of CD
- 10. If the moving line x = A and the function f (x) = SiNx and G (x) = cosx intersect at M and N respectively, then the maximum value of | Mn | is___ .
- 11. To find the second root formula of the first 3: a > 0 > b, simplify the root sign (a square - 4A + 4) + root sign (1,4 + B + b square) 3>a>2>0>-1>b>-2
- 12. If ABC is the triangle ABC three sides, simplify the square of (a + B-C) under the root sign - the square of (a-b-c) under the root sign
- 13. If x, y satisfy y
- 14. The third power of the root a divided by the root AB times the root B fraction a
- 15. Why is the second power of minus half equal to the root two? The definition written in the textbook is y = a x power (a > 0) minus half is not less than zero
- 16. The 2002 power of (Radix 2-radix 3) is multiplied by the 2003 power of (Radix 2 + Radix 3)
- 17. The image of the first order function y = (- radical 3 / 3) x + 1 intersects with X axis and Y axis respectively at two points a and B. taking line AB as the edge, an equilateral triangle ABC is made in the first quadrant (1) Find the area of ABC (2) if there is a point P (a, 1 / 2) in the second quadrant, try the formula containing a to represent the area of quadrilateral ABPO, and calculate the value of a when the area of triangle ABP is equal to that of triangle ABC
- 18. Let a = radical 8-x, B = radical 3x + 4, C = radical x + 2. If a, B, C are the three sides of a right triangle, find the value of X I'm not sure how to determine the maximum side
- 19. Given that the domain of the function f (x) = 2Sin ^ 2x - (2 radical 3) sinxcosx-1 + radical 3 is [0, Pai / 2], then the value range of y = f (x) is?, and the zero point is?
- 20. Move the factor outside the root sign into the root sign: a root sign minus 1 / A fast