Points a and B represent real numbers a and B respectively on the number axis. The distance between two points of a and B is expressed as ∣ ab ∣. Then | ab | = | b-a| (1) If two points a and B on the number axis represent real numbers x and - √ 2 respectively, and ab = 3, find the value of X (2) If the three points P, a and B on the number axis represent real numbers x, - 2 and √ 3 respectively, the value range of X is obtained when the algebraic formula | x + √ 2 | + | X - √ 3 | takes the minimum value

Points a and B represent real numbers a and B respectively on the number axis. The distance between two points of a and B is expressed as ∣ ab ∣. Then | ab | = | b-a| (1) If two points a and B on the number axis represent real numbers x and - √ 2 respectively, and ab = 3, find the value of X (2) If the three points P, a and B on the number axis represent real numbers x, - 2 and √ 3 respectively, the value range of X is obtained when the algebraic formula | x + √ 2 | + | X - √ 3 | takes the minimum value

Guo Dunyong replied:
（1）∵|－√2－x|=3,
When | - √ 2-x | > 0, - √ 2-x = 3, x = - 3 - √ 2 = - 4.4142;
When | - √ 2-x ＜ 0, √ 2 + x = 3, x = 3 - √ 2 = 1.5858
(2) When | x + √ 2 | + | X - √ 3 | is the minimum value, the value range of X is: [- √ 2, √ 3]
Xmin = √ 2 + √ 3 = 3.1463