I hl t jl tj <
V^y bat phuang trinh c6 nghi^m duy nhat x=1 +Vs * Cach 3:
b) Dieu kỉn: x > -2 . '
Ta Viet lai bat phucmg trinh thanh: x^ - 3x(x + 2) + 2^J{x + 2f < 0 '
+ Xet truong hg^p: x = -2 khong thoa man bat phuang trinh:
+ Xet x > -2. Ta chia phuang trinh cho ^J{x + 2f > 0 thi thu dug'c:
/ N3
Vx + 2 - 3 sfx + 2 + 2<0
Dat t = ^ ta CO bat phuong trinh: t^ - 3t + 2 < 0 <=> (x - l)^(x + 2) < 0 t = l t = l t^-tl <» t < - 2 + Giai t = 1 <=> t = l t < - 2 NArr2 0 -í x>0 x 2- x - 2 = 0 <=>x = 2 + Giai t < -2 <=> < -2 <=> - X > ly[x + l
Ket hp-p (1) va (2) ta suy ra nghi^m aia bát phuang trinh la: x ^ - 2 x ^ - 2
x^O <=>2-V3<x<0
x^ - 4 x - 8 > 0
2-V3<x<0
x = 2
Chii y: Khi giai bat phuang trinh: ẬB > 0 o A = 0
B>0 HQC sinh thuang mac sai lam khi chi giai B > 0. HQC sinh thuang mac sai lam khi chi giai B > 0.
d) Dieu ki^n x > -2 * Cachl: * Cachl:
Ta viet lai bat phuang trinh nhu sau: (x^ + 4)V2x + 4 + x^ + 4 ^ 4x^ + 6x
o (x^ + 4)(N/2X + 4 +1) < 2x(2x + 3) «> (x^ + 4)(V2x + 4 +1) ^ 2x{^{l\ Af -1)
«> (x^ + 4)(V2x + 4 +1) < 2x(V2x + 4 + l)(>/2x + 4 -1)
Qo -f2x + 4 +1 > 0 . Bat phuang trinh da cho tuong duong vai
<ji> + 4 < 2x(V2x + 4 -1) » x^ + 2x + 4 - 2xV2x + 4 < 0 ^x - ^Jlx + X^ <, 0
J ^ v = l + V5
<-,x = \/2x + 4 <=><! - <=>x [ x 2- 2 x - 4 = 0
Cach 2: Bat phuang trinh tuang duang vai:
2 + 4)V2x + 4 < 12x2 ^ 24x -16 . D5t t = V2x + 4 => x =
4(x
trinh da cho tro thanh: [(t^ - 4)^ +16
t ^ - 4 Bát phuang
t<3( t 2-4) 2+12( t 2-4)-16
t<3(t2 -4)2 +12(t2 - 4 ) - 1 6 o t 5 -3t'' -St^ +12t2 +32t + 16<0
c> (t + l)(t"* - 4t^ - 4t2 + 16t +16) < 0. Do t > 0 nen bat phuang trinh tuong
duang vai: t"* - 4t^ - 4t'^ + 16t +16 < 0
Neu t = 0 o X = -2 khong thoa man bat phuang trinh. Neu t > 0. Chia bat phuang trinh cho t^ > 0 ta thu dugc: Neu t > 0. Chia bat phuang trinh cho t^ > 0 ta thu dugc:
o t 2 - 4 t - 4 + l^ +t t^ iJ<0« ( 4 ' t — - 4 t - - + 4 < 0 o t - - - 2 2 r 4^ -r 4>
I h l tj l tj <0
o t - - ^ - 2 = 0<=>t2-2t-4 = 0«t = l + > / 5 o x = l + >/5 a r ;. v-
V^y bat phuang trinh c6 nghi^m duy nhat x = 1 + Vs * Cach 3: * Cach 3:
(X2+4)V2X + 4<3X^+6X-4O(X2+4)(N/2X + 4+I)<2X(2X + 4-1)
(x^ + 4)(V2x + 4 +1) < 2x(V2x + 4 +1)(V2x + 4 -1) o x^ + 4 < 2x(V2x + 4 -1) o x^ + 2x + 4 < 2xV2x + 4 n o x^ + 2x + 4 < 2xV2x + 4 n
Theo bat ding thuc AM-GM ta c6: 2xV2x + 4 <2|x|VIx+I< x^ + 2x + 4 = >/2x + 4 = >/2x + 4
Dau bang xay ra khi va chi khi X
x>0 o X