MC vdi (O) (C la tiep diem) Ke CH vuong goc vdi AB (He AB), MB cat
b) Ti mm de phiTdng trinh (1) c6 hai nghi$m Xi,X2 thoa man:
X1X2- 2(x, + X2) = 4
Bai 3: (1,5 diem) Quang difcJng AB dai 120 km. Hai xe may khdi hanh cilng mot luc di tif A den B. Van toe cua xe thuf nhat Idn hcfn van toe cua xe thit hai la 10 km/h nen xe may thu" nhat den B triTdc xe thuT hai 1 gid. Tinh van toe cua moi xẹ
Bai 4: (3,5 diem) Cho diem A n^m ngoai dtfdng tr6n (O). Tit A ke hai tiep tuyen AB, AC va cat tuyen ADE tdi dirdng tron do (B, C la hai tiep diem ; D
nkm giffa A va E). Goi H la giao diem cua AO va BC. a) ChiJng minh r^ng .ABOC la tu" giac npi tiep.
b) ChiJng minh rkng AH.AO = AD.AẸ
c) Tiep tuyen tai D cua difdng tron (O) c^t A B , AC theo thỉ tU" tai I va K. Qua diem O ke diTdng thing vuong goc vdi OA dl AB tai P va c^t AC tai Q. ChiJng diem O ke diTdng thing vuong goc vdi OA dl AB tai P va c^t AC tai Q. ChiJng minh rling : IP + KQ > PQ.
Cty TNHH MTV D W H Khang Vi$t
HUONG D A N G I A I B a i l : B a i l : a) A xac dinh <=> • X > 0 X - Vx 9t 0 X > 0 ^ / x - l 7 t 0 <=> <^N/X(VX - 1) ?t 0 O • N/X + 1 ^ 0 ^[x ^ 1 x > 0 X ^ 1" Vay D K X D cua A la x > 0 va x ;t 1. 2 A = 1 ^ V x+ 1 1 + Vx ( ^ / x- l ) V x- 1 3 Vx 3 r / - 3 9 < o 2 V x = 3 0 Vx = - c : > x = - (thich hrtp) 2 4 1 9 Vay A = - khi X = —. 3 4 n,fí- \ r ) A n r > / x - l r - V ' x - 1- 9 X c) P = A - 9 V x = —1= 9Vx = p ^yx , VX '. " ^ _ - ( 9 x- 6 V ^ + l ) ^ -5^ ^ -(3N/^ - if ^ ^ ^ >x fifiis jXití' V i ^ ^ " ^ < 0, vdi moi X > 0 vx Dau " = " xay ra o 3 Vx - 1 = 0 o >/x = - » X = - . ^Lll: 3 9 J Vay gia tri Idn nhát cua bieu thiJc P bcHng - 5 . , r,
Nhan x e t: Cau a), b) de, quen thupc ; cau c) neu xem Vx = X ta nhan ra :
—QY^ J. V _ I
P = — (vdi X > 0), tir do de tim diTdc Idi giai nhiT tren. X X
fiai 2: a) Khi m = 1, phu-dng trinh (1) trdlhanhx^- 6x + 8 = 0, Á = 9 - 8 = 1, VÁ = 1. * 3 + 1 3 ^ 1 Phtfcfng trinh c6 hai nghiem phan bict la: X| = ^—— = 4 ; X: = = 2.
1 1
Luy$n giai dfi truflc kl thi vko lap 10 ba mign B^c, Tmng, Nam mOn ToAn _ NguySn Dure la'n
PhiTcfng i r i n h (1) c6 h a i nghiem x,, X 2 <=> Á > 0 <=> 4 m - 3 > 0 <=> 4m > 3 <=> m > — 4 Theo he thuTc Vi-et, ta c6 < X | X 2+ X , = = m^ + 7 2(m + 2)
Do do X 1 X 2 - 2( X | + X 2 ) = 4 <=> + 7 - 4(m + 2) = 4
"'"'•A
C m' + 7 - 4 m - 8 = 4 <^ m - 4 m - 5 = 0 (*) m' + 7 - 4 m - 8 = 4 <^ m - 4 m - 5 = 0 (*)
V i a - b + c= l - (-4) + (-5) = 0 nen (*) c6 hai nghiem mi =-1 ; m2 = - - = 5. a
• - 1 < —nen m = - 1 (loai) • 5 > — nen m = 5 (nhan) ' * r 4 • 4
Vaym = 5.
Nhan xet : Day la bai toan ve phi/cfng trinh bac hai, van dung he thtfc Vi-ct
rat quen thuoc dói vd'i moi hoc sinh.
Bai 3: Goi van toe eua xc thỉ hai la x (km/h) (Dieu kien x > 0) Van tóc cua xc ihiJ nhat la x + 10 (km/h)
120
Thdi gian xe thỉ nhat di tif A den B la : 120 : (x + 10) = (h)
x + 10 120
Thdi gian xe thỉ hai di tuf A den B la : 120 : x = (h)
X
Xe thu" nhat den trifde xe thiJ hai 1 gid, nen ta eo phifOng trinh : 120 120
X + 10 = 1 120(x + 10) - 120x = x(x + 10) o 120X+ 1 2 0 0 - 120x = x^+ 10xox^ + lOx- 1200 = 0
Á = 25 + 1200 = 1225, VA' = 35
X] = ^ I - 30 (thich hop); X2 = ^ = -40 (khong thich hdp) Vay van toe cua xe Ihu" hai la 30 km/h ;
Van toe cua xe thu" nhát la : 30 + 10 = 40 (km/h)
NhSn x^t : Giai bai toan bang each lap phiTdng trinh loai toan chuyen dong. day eung la dang loan quen thuoc. LUU y r^ng : Neu xe thiJ nhát ve trtfdc (vc sdm), phifdng trinh can lap la : txdhiJhai - txethenha-i = tv^rfm
Bai 4: