Simplified evaluation: (2x-y) 13 △ [(2x-y) 3] 2 △ [(y-2x) 2] 3, where x = 2, y = - 1

Simplified evaluation: (2x-y) 13 △ [(2x-y) 3] 2 △ [(y-2x) 2] 3, where x = 2, y = - 1

When x = 2, y = - 1, the original formula is 2 × 2 - (- 1) = 5

If we take any two numbers a and B in the interval [0,1], then the probability of zero free function f (x) = x2 + ax + B2 is ()
A. 12B. 23C. 34D. 14

In the interval [0, 1], take any two numbers a, B, the function f (x) = x2 + ax + B2 has no zero ⇔ x2 + ax + B2 = 0 has no real root, a, B ∈ [0, 1] ⇔ △ = a2-4b2 ＜ 0, a, B ∈ [0, 1]. According to the constraint condition a, B ∈ [0, 1] A2 ＜ 4B2, draw the feasible region: the probability p = 1-12 × 1 × 12 = 34 of the function f (x) = x2 + ax + B2 has no zero

Help me to solve the second mathematics of junior high school and substitute it into the elimination method to solve the equations: ① {x + y = 7,3x-17 = - y}, ② the solution of half X-Y = half, x + Half y = - 9

x+y=7①
3x-17=-y②
From ②, we can get: 3x + y = 17 ③
(3) - 1: 2x = 10
　　x=5
Substituting x = 5 into (1) yields 5 + y = 7
　　y=2
　∴x=5
　　y=2
x/2-y=1/2①
x+y/2=-9②
X-2y = 1 (3)
2 × 4: 4x + 2Y = - 36 4
(3) + (4): 5x = - 35
　　x=-7
Substituting x = - 7 into 3 gives: - 7-2y = 1
　　y=-4
　∴x=-7
　　y=-4

Given that the image of a quadratic function passes through (3,0), (2, - 3) points and the axis of symmetry x = 1, the analytic expression of the function is obtained
You'd better thank me before 9 o'clock today

9a+3b+c=0
4a+2b+c=-3
-b/2a=1
Solution
a=1
b=-2
c=-3
y=x^2-2x-3

Y = x ^ 2-2x-3 = (x-1) ^ 2-4 ≥ - 4 Why do we finally get ≥ - 4? Where is x?

Because: no matter what value x takes, (x-1) ^ 2 can only be a number greater than or equal to 0
A number greater than or equal to 0 minus 4 must be greater than minus 4
So you have the inequality
The minimum value of (x-1) ^ 2 is 0
The minimum value of (x-1) ^ 2-4 is - 4

Given that the equation (m-2) x | m | - 1 + 3 = 5 is a linear equation of one variable with respect to x, then the value of M is ()
A. + 2B. 2C. - 2D. Not sure

According to the definition of one variable linear equation, we can get: | m | - 1 = 1, and m-2 ≠ 0, we can get m = - 2, so we choose C

x- 0.8x = 16+6

x- 0.8x = 16+6
0.2x=22
x=110

Given the position of real numbers a and B on the number axis as shown in the figure, try to simplify
|a|+√（a^2）-√（b^2）
━━┷━━┷━━━━━┷━━━━》
a 0 b

=-a+（-a）-b=-2a-b
a0 √（b^2 =b

(3x-4) * 5 is equal to 4, help to calculate, thank you

Linear Algebra: practical significance of facing matrix and positive definite matrix?
Do symmetric matrices and positive definite matrices have any practical significance? Why do linear algebras study them? Do they create pairs of matrices and positive definite matrices for some properties?

This is mainly for practical application
Symmetric matrix and Hermite matrix are mainly introduced to study self adjoint operators. In practice, a large number of operators are self adjoint, both in classical mechanics and quantum mechanics. A large number of self adjoint operators are positive qualitative, which mainly describe some physical quantities (such as distance, mass, etc.) that must be positive
Many concepts in mathematics, especially the older ones, generally come from practical problems, because the discovery of some special properties enables these concepts to be preserved and used for separate research