+ Diem mau chot ciia phuong phap nay la phai chpn mpt biéu thuc f(x) de dat f(x) = t sao cho phan con lai phai bieu dien dupe theo an t . NhOng bai toan dang nay noi chung la dẹ
+ Trong nhieu truong hpp ta can thuc hi^n phep chia cho mpt bieu thuc c6 san 6 phuong trinh tu do moi phat hi^n an phụ Tuy thupc vao cau true phuong trinh ta c6 the chia cho g(x) phu hpp (thong thuong ta chia cho x'' voi k la sóhOu ty)
+ Doi voi nhirng bai toan ma vi^c dua ve mpt an dan den phuong trinh moi phuc tap nhu: So mu cao, can bac cao .. thi ta c6 the nghi den huong dat nhieu an phu de quy ve h? phuong trinh hoac dya vao cac hang dSng thuc de giai toan.
Ta xet cac vi dy sau:
V i dy 1; G i a i cac phuong trinh sau:
a) x^ =(1-N/^)(2X-3N/X+3) ^ ^ b) x^ + N/X^^V" = 2x +1
c) x + l + Vx^ -4x + l =3s[\'
Giai:
a) Dieu ki^n: x > 0. Phuong trinh da cho c6 the viet leii nhu sau:
T m Hfw on ini uui nyi sung Tooim-gmr-n^ nui rx,nif r i, QUI T J I - i\guyen i rung t^^^
khong phai la nghi^m ciia phuong trinh. Ta chia hai ve cho thi thu 1- V x
dugc: 1 = 2 1-^ + 3 . Dat - — ^ = t ta CO phuong trinh theo t :
3t^ + 2 t- l = 0 o t = - l t = l 3 Truong h(?p 1: t = - l taco: ^ — ^ =-1 o x - +1 = 0(VN) Truong hgp 2: t = — ta c6: 3 l ^ = l « x - 3 V ; ^ - 3 = 0« r 3 - N / 2 T , - , ,— =>x = ^ ^ 3 + j v ^ 2
Ket luan: Phuang trinh c6 nghi^m duy nhát: x = 15 + 3N/2T
b) Ta thay x = 0 khong phai la nghi^m ciia phuang trinh. Vi vay ta chia hai ve cho x thi thu dugic: x + s / x - —=2 + — o x - i + s / x - —- 2 = 0
V X X X V X
D§t t = ^ x - — ta t h u duQC p h u a n g trinh:
t ^ + t - 2 = 0 o t = l = > x - i = l o x ^ - x - l = 0 o x = ^ ^ ^ o
Ket luan: Phuang trinh c6 nghi^m x = c) Dieu kif n: x > 0
x^ - 4x + l> 0
0 < x < 2 - V 3
x>2 + S
Ta thay x - 0 khong phai la nghifm cua phuang trinh. Chia hai ve cho
ta thu dugc: yfx + + . x - 4 + —= 3. Dat t = Vx + =>t^ = x + — + 2 theo
Vx V X X
bat dang thuc Co si ta c6 t > 2 . Thay vao phuang trinh ta c6:
Hy ft ^ 3 5
V t 2- 6 = 3 - t c ^ ^ , , o t = -
t 2 _ 6 = t - 6 t + 9 2
C t y INHHim-yUWHKhang VifT'
< = > 3 ^ = x + - + 2 < = > 4 x ^ - 1 7 x + 4 = 0<i> 4 X x = 4 1 X = — 4 Ket luan: Phuong trinh c6 2 nghifm: x = 4,x = — V i dy 2: G i a i cac phuang trinh sau:
a) (13 - 4x)V2x - 3 + (4x - 3)75 - 2x = 2 + 8yjl6x - Ax^ - 1 5 b) 7 V 3; t: - 7 + ( 4 x - 7 ) ^ / 7 ^ = 32 b) 7 V 3; t: - 7 + ( 4 x - 7 ) ^ / 7 ^ = 32
Giai: , , 3 5