au* bv : ub+ uv o lu -b)( u-a ) : 0
o Bdng c6ch cho trudc
(.,m-r,XJ,*r -0=o (14)
Bitin d6i PT (14) thenh
Jx+3+z*Jx+t=2x+J7 +4x+3 (15)
Nhu vfly dC giai PT (15), ta bitin AOi rr 1tS)
,re Pt 1i+1, tu d6 tim dugc An x.
o Tuong t.u, ft (Jx'+l-rXr-r)=o ta dusc
1,r*J*z-rr1:J*: +t+* (16)
Ve dC cho bii to6n tro 16n kh6 hon, ta sE bitin COi pf (16), ching hpn nhdq hai vti ctra PT
(16) v6i i"qng hen hqrp cira v6 phii, quy d6ng ta dugc PT m6i ld
(r*r$'*r[Jx'+r -x) :t.
B6ng c6ch ldm tuong t.u, ta dugc mQt lopt c6c PT kh5c. Sau ddy ld mQt s6 bdi tflp tl6 nghi.
Gidi cdc phuong trinh sau:
a) xJx+8 + (x+z)'[x+z=*'+2*+"[7 +10ffi ;a) z*J x+z +J z* +n x+t=z*J x+t+',| * +to*x ; a) z*J x+z +J z* +n x+t=z*J x+t+',| * +to*x ; q ^,17 +* +z***Jx =Jl"+l +JI* +x ; r- e; !tl1*2 *$A =z+Jrx'z +sx-3. x (1 1)
Xem PT (11) ld PT b$c hai 6n LtinhbiQt thirc
A' theo x ta dugc
L' =1*2x)' +Q x-t)= +x2 +3 x .
Ta th6y A' kh6ng la binh phuong cira da
thirc, di6u d6 sE ldm cho ngudi giii tro l€n
tOi rOi. Nhu vfly <te giai PT (11) mOt c6ch d6
ddng, ta bi6n d6i PT (11) trd thdnh PT (8),
sau d6 d4t t=J+x'++ sE dugc PT bflc hai
theo I c6 A' ld binh phuong cria da thric, khi
d6 bi6u diSn du-o. c I theo x, tu d6 ta tim
dugc x.
Bing c6ch ldm tuong t.u, ta du-o. c mQt lopt c6c
PT kh6c. Sau ddy li mQt sO bdi tfp dC nghi.
Gi6i c6c phuong trinh sau:
a) l5x2 +?\x+llJ x+2=2-5x I O, *+2+*Jir+l =,{*+z; ' x+l|2x+l c) 3x2 +2x+3=Qx+f}/7+3 ; d) l2 +3x+ +=(r+l)J7+*+2 ; e) (3x+r)rEx'? -1 =5x' +1x-3. 2
III. XuAt phrlt tir tinh ch6t nghiQm ciia
phuong trinh bflc hai
Ta tI1 bi6t x=xr vd" x=xz ld nghiQm ciraphuong trinh bfc hai phuong trinh bfc hai
*'-(*r+ x2)x+4x2=0.
r Bing c6ch cho tru6c nghiQm cria PT bflc
hai ld *=JA vd x=Jx+2 ta dugc
x' -(.,6+t + J.+z)-*J * *2.+z=o (12)
o Bing c6ch cho tru6c nghiQm cira PT bflc
hai ld x=J16a2 v| v=-.,[a] ta tlugc
*, -(lii -Jr*3)r.Jr'.sr*6 =o (13)o DO ldm bdi to6n tro 16n kh6 h<vn, ta biOn d6i o DO ldm bdi to6n tro 16n kh6 h<vn, ta biOn d6i
PT vria c6 dugc, ching h4n tu PT (12) ta
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3x-15 5-;
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---J-+(x-5X3x+l)=0
V3x+1+4 J6-x+l o Tu phucrng trinh .od+*rr)=cos3r, bi6n
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