2.Vậy :
S ={ }
72; 2 . e)
(2
x−5
)2
−
(x+2
)2
= ⇔0
(2
x− − −5
x 2
)(2
x− + +5
x 2
)=0 ⇔(
x−7 3)(
x− =3) 0− = = 7 0 7
x x⇔ − = ⇔ =3 3 0 1.Vậy :
S =
{ }
7;1 . f)
x2
− −
x (3
x− = ⇔3) 0
x x( − −1) 3(
x− =1) 0( )( ) 1 0 1⇔ − − = ⇔ − = ⇔ =1 3 03 0 3.Vậy :
S =
{ }
1;3 .
Ví dụ 4. (Bài 23, trang 17 SGK) Giải phương trình : a)
x(2
x− =9) 3
x x( −5); b) 0, 5
x x( − =3) (
x−3 1, 5)
(
x−1
)
;c) 3
x−15=2
x x( −5); d) 3 1 ( )1 3 77
x− = 7
x x− .
Giải a)
x(2
x− =9) 3
x x( − ⇔5)
x(2
x− −9) 3
x x( − =5) 0(2 9 3 15) 0 ( 6) 0⇔ − − + = ⇔ − + =
x x x x x= =0 0⇔− + = ⇔ =6 0 6.Vậy :
S =
{ }
0; 6 . b) 0, 5
x x( − =3) (
x−3 1, 5)
(
x− ⇔1
)
(x−3 0, 5
) x−
(x−3 1, 5
)(
x− =1
)
0(
x 3 0, 5)
(
x 1, 5
x 1
)
0⇔ − − + = ⇔(
x−3)(− + =
x 1) 0 3 0 31 0 1.c) 3
x−15=2
x x( − ⇔5) 3(
x− −5) 2
x x( − =5) 0 = − = 5 0( )( ) 55 3 2 0 33 2 0 .2Vậy :
S={ }
5;32 . d) 3 1 ( ) ( )1 3 7 3 7 3 77
x− = 7
x x− ⇔
x− =
x x− ⇔(3
x− −7)
x(3
x−7)=0− = = (
3 7 1)( )
0 3 7 0 731 0