Inspired by "shower faucet", Mr. Li made up a topic: intercept the corresponding line AB from 0 to 3 on the number axis, and the real number m corresponds to the point m on AB, as shown in Figure 1; fold AB into an equilateral triangle, so that the points a and B coincide with the point P, as shown in Figure 2; establish a plane rectangular coordinate system, translate the triangle, so that it is symmetrical about the Y axis, and the coordinates of point P are (0,2), PM and X axis intersect at point n (n,0) ）When m = 3, find the value of N. when you solve this problem, the value of n is () A. 4-23B. 23-4C. −233D. 233

Inspired by "shower faucet", Mr. Li made up a topic: intercept the corresponding line AB from 0 to 3 on the number axis, and the real number m corresponds to the point m on AB, as shown in Figure 1; fold AB into an equilateral triangle, so that the points a and B coincide with the point P, as shown in Figure 2; establish a plane rectangular coordinate system, translate the triangle, so that it is symmetrical about the Y axis, and the coordinates of point P are (0,2), PM and X axis intersect at point n (n,0) ）When m = 3, find the value of N. when you solve this problem, the value of n is () A. 4-23B. 23-4C. −233D. 233

∵ AB = 3, △ PDE is equilateral triangle, ∵ PD = PE = de = 1, take the vertical bisector of de as y axis to establish rectangular coordinate system, ∵ PDE is symmetric about y axis, ∵ PF ⊥ De, DF = EF, de ∥ X axis, ∵ pf = 32, ∵ PFM ∽ PON, ∵ M = 3, ∫ FM = 3-32, ∫ pfop = fmon, that is 322 = 3 − 32on, the solution is on = 4-23

Given that the opposite number of a root of x2-4x + B = 0 is the root of x2 + 4x-b = 0, find the positive root of x2 + bx-4 = 0

The solution is: B ≤ 4, x = 4 ± 24 − B2 = 2 ± 4 − B, that is: X1 = 2 + 4 − B, & nbsp; & nbsp; & nbsp; If x 2 = 2-4 − B; ∵ x 2 + 4x-b = 0 has a root, then ∵ 2 = 16 + 4B ≥ 0, the solution is: B ≥ - 4, substituting - x 1 = - 2-4 − B, - x 2 = - 2 + 4 − B respectively into the equation x 2 + 4x-b = 0, the solution is: B = 0, which is in line with the meaning of the problem. Substituting B = 0 into x 2 + bx-4 = 0, the positive root is: x 2

Given that a is a root of X & # 178; - 4x + 1 = 0, then the value of 1 / 2 of A-A is?

x²-4x+1=0
x²-4x+4=3
（x-2）²=3
x=2±√3
a=2±√3
a-1/a
=（2+√3）-1/(2+√3）
=（2+√3）-（2-√3）
=2√3
or
a-1/a
=（2-√3）-1/(2-√3）
=（2-√3）-（2+√3）
=-2√3