Phuang trinh dugc viet lai nhu sau:
7( V 2 x- 3 + V 5- 2 x ) -2 r( 2 x - 3) V 2 x- 3 + ( 5 -2 x) V 5- 2 x = 2 + 8 V( 5- 2 x ) ( 2 x- 3 )
Dat
t = V 2 x- 3 + V 5 - 2 x= > 7( 5- 2 x ) ( 2 x- 3 ) = - - . Dieu kỉn (N/2 < t< 2 . 2 ^ '
Phuong trinh da cho c6 dang: t ' ' - 4 t ^ + t + 6 = 0=>t = 2=>x = 2
Ngoai ra ta cQng c6 the giai phuong trinh tren bang each dua ve hf. 7 . . b) Dieu kif n: — < x < 7 .Phuang trinh da cho dugc viet lai n h u sau:
3
i( 3 x - 7 ) + | ( 7 - x ) V 3 X - 7 l ( 7 - x ) + | ( 3 x - 7 ) V 7 - X =32 ^(3x-7) + ( 7 - x) ] V 3 x- 7 + [ ( 7 - x ) + ( 3 x - 7 ) ] V 7 ^ = 64 D|tt = x/3x-7 + % / 7 ^
=> t^ = {3x - 7 ) V 3 x - 7 + (7 - x ) V 7 ^ + 3 7( 3 x - 7 ) ( 7 - x ) ( V 3 x - 7 + N /T ^ )
T u phuang trinh suy ra t^ = 64 o t = 4 . Hay V 3 x- 7 + V 7 - x = 4 Binh phuong 2 ve ta thu dugc:
V( 3 x- 7 ) ( 7 - x ) =8-x<=>4x2 - 44x +113 = 0 <=> x = 11±2N/2
Tai sac ta phan tich dugc hai phuang trinh n h u tren: Ta thay voi nhiing phuang trinh:
(ax + b)7cx + d + (ex + h)^gx + k + r^(cx + d)(gx + k) + s = 0 thi mgt trong nhCrng each x u ly kha hi^u qua la:
mi nyu uti till iTin i,or smfg-rmnmgiut Íl, pat Íl, Íl, oai tji -i\guyen imugKten
Phan tích: ax + b = m(cx + d) + n(gx + k) va ex + h = m '(cx + d) + n '(gx + k) sau do ta c6 the d | t an phy tr^c tiép, ho|ic d^t hai an phy de quy ve h§. V i d y : * ;
K h i giai phuong trinh: ^ ,^j ^.
(13 - 4x)72x - 3 + (4x - 3)V5 - 2x = 2 + 8\/l6x - 4x^ - 1 5 ta thuc hỉn cac phan tich :
+ G i a s u : 1 3 - 4 x = m(2x- 3 ) + n(5-2x).- "
Dong nhat hai veta suy ra: • 2m - 2n = -4 3 7 <=> m = —,n = — - 3 m + 5n=13 2 2
7 3 + Tuong t u ta gia sir: ( 4 x - 3 ) = m'(2x- 3 ) + n ' ( 5-2x) = > m ' = - , n ' = -
K h i giai phuang t r i n h : 7 V 3 x - 7 + (4x - 7 ) ^ 7 - x = 32.
Ta thuc hi^n phan tich: m(3x - 7) + n(7 - x) = 7 va p(3x-7) + q ( 7 - x ) = 4 x - 7
, 1 3 3 1
Sau do dong nhat 2 vede tim m, n, p, q ta c6: m = —; n = —; p = —; q = — N h u vay ngoai each dat an phu nhu tren ta c6 the giai cac bai toan theo each khae n h u sau:
a) Dieu kien — < x < —.
' 2 2
Dat a = 7 2 x^ , b = thi â + b^ -2 .
T u each phan tich tren ta c6 h^ sau:
(a + b r - 2 a b = 2 a ^ + b ^ = 2 a ^ + b ^ = 2
(33^ + 7b^ )a + (3h^ + 73^ )b = 4 + 163b 3(3 + b)^ - 2ab(3 + b) - 163b - 4 = 0
(a + b)^ - 2ab = 2
3(a + b)^ + 2- ( a + br (a + b) + 8 2- ( a + br - 4 = 0
D | t a + b = S,ab = P dieu ki^n S,P >0;S^ > 4P.
Ta CO h^ moi sau: • - 2 P = 2 S = 2
2 5 ^ - 8 5 ^ + 2 5 + 12 = 0 [P = 2 b) Dat a = \l3x-7, h = yj? -x ta c6 h^ phuong trinh
<=> a = b = 1 <=> X = 2
(a + b f = 6 4 Ja + b = 4
a 2 + 3 b 2= 1 4. ^ K+ 3 b 2= 1 4 .
Giai h^ phuong trinh ta thu dugc: a,b => x .