Question

[Phạm Hồng Quyên]

tìm x biết | x-2 | + | x+3 | = 5

Cần gấp ạk, thanks m.n nhìu lm 

Answer 1

[An Hoà]

| x - 2 | + | x + 3 | = 5

| x - 2 | = | 2+ x |  ,     | x + 3 | = | 3 - x |

Ta có :

| x - 2 | + | x + 3 | = |2 + x | + | 3 - x | >=|2 + x + 3 - x | = | 5 |

=>| x - 2 | + | x + 3 | >= 5

Dấu ( = ) xảy ra khi :  ( 2 + x ).( 3 - x )>=0

TH1:

2 + x >= 0                                               3 - x >= 0 

  x     >= - 2                                                  x <=3

=> x rỗng

TH2:

2 + x <=0                                                 3 - x <=0

      x<=-2                                                      x>=3

=> 3 <= x <= - 2

Vậy 3 <= x <= - 2 thì | x - 2 | + | x + 3 | = 5