D thing hang.
A (x ,y)e( P)
yA = 9
1) . N e n 9 = X A o X A = ±3
Cty TNHH MTV DWH Khang Vi$t
A G (d) 9 = m.3 9 = m . ( - 3 ) <=>
m = 3 m = - 3 m = - 3
Vay m = 3 hoSc m = - 3 thi (P) va (d) c^t nhau tai diem c6 tung dp b^ng 9.
2) PhÚCng trinh hoanh do giao diem cua (P) va (d) la ,, , , ,, ,, = mx <=> X - mx = 0 <=> x(x - m) = 0 = mx <=> X - mx = 0 <=> x(x - m) = 0 X = 0 X - m = 0 X = 0 X = m v'T , X = 0 thi y = 0. Vay 0(0; 0) . X = m thi y = m^. V a y A ( m , m^) Ta CO O A = V ( m - 0)^ + (m^ - 0)^ = V n / T m ^ O A = ^/6 <=> yjm'* + m^ = V6 o m"* + m^ = 6 4 2 1 ^ 1 < : > m + m + - = 6 + - c : > 4 4 o m ^ + - = - < : > m ^ = 2 o m = ± V 2 ' 2m + - I ' ' V 2, 25 4
Vay m = yfz hoSc m = -yfl thi (P) v i (d) c^t nhau tai hai diem ma khoang cdch giijra hai diem nay b^ng \f6 .
N h S n x e t :
1), 2) la dang bai toan quen thuoc.
3) Chii y rang neu A ( X A , yA), B ( X B , ye) thi A B = ^ ( x g -^AY + ( y s - y A ) ^
c6 the chtfng minh dieu nay r o i van dung de giai bai todn that chSc chẹ Cfiu 3.
1) P = V 3- 1
2 - V 3 2 + yl3j3-S
2 + V3 V 3 - I
4 - 3 4 - 3
2. Ta CO (â + b^) - (âb^ + âb-^) = â - âb^ + b^ - âb' = a-^â - b^) - b^(â - b^) = (â - b^)(â - b^)
Luy§n giSi dS traflc ki thi vko Idp 10 ba m\in Bac, Trung. Nam mOn Toan _ "JgD.f: f i i f . ian_
Vi a + b > 0, (a - b)^ > 0, a + —
2J
Dod6 (â +b^)>âb^ + âb^
Nhan xet: 1), 2) \h dang b£li toin quen thupc dilng cdc phep bien đi tiTcfng
diTcfng de giai bai loan 3(2) "
Cfiu 4. 1. Ta CO AHE = ACH (cung phu vdi goc CHE) 0
AHE = ADE (Hai goc noi tiep cilng ch^n cung AE) Dodo ADE = A C H .
Vay ttf giac BDEC npi tiep. 2) Ta CO DAE - 90" (gt) ^ DE la
diTctng kinh cua difdng tr6n (O) Vay ba diem D, O, E thing hang. 3) AABC vuong tai A
=> AB^ + AC^ = BC^ (dinh li Py-ta-go) Do d6 3^ + AC^ = 5^ AC^ = 16 => AC = 4 AABC vuong tai A, AH la drfcfng cao => AH.BC = AB.AC o AH.5 = 3.4 => AH =
" ;dl Ị'!
'm
12 DE = A H = y . DE = A H = y .
X6t AAED AABC, ta c6: DAE (chung), ADE = ACB chỉng minh tren) D o d o A A E D ' ^ AABC(g.g) SAED SABC BC 144 625 SABC = - A B . A C - -.3.4 = 6 2 2 *'"l44 144 , 864 Nfin SAED = — S A B C = — . 6 = 625
SBDEC = SABC - SADE = 6 -
625 625 864 864
625 = 4,6176 (cmO
Nhan xet: Day la bai loan hinh hoc de, quen thuoc.
Cty TNHH MTV DWH Kh;iiig V i e t
Dt. S 6 4 6
T H I T U Y E N S I N H V A O LdP 1 0 C H U Y I N T I N H D 6 N G N A I N A M H O C 2 0 1 2 - 2 0 1 3
C&u 1- (1'5 diem) Cho phiTcJng trinh x"* - 16x^ + 32 = 0 (vdi x e R)
ChiJng minh r^ng x = yj6 - 372"+^ - yfz + 'JTT^ la mpt nghiem cua phiTOng trinh da chọ
f2x(x + l)(y + 1) + xy = -6 ' *
Cfiu 2. (2,5 diem) Giai h$ phUdng trinh
2y(y + l)(x + 1) + yx 6 (vdi x e R, y 6 R)
Cfiu 3. (1,5 diem) Cho tam giac deu MNP c6 canh bkng 2cm. Lay n diem thuSc
cac canh hoSc d phia trong tam gidc deu MNP sao cho khoang each giiJa hai
diem tuy y Idn hdn 1cm (vdi n la so nguyen dúdng). Tim n Idn nhát thoa man
dieu kien da chọ \
Cfiu 4. (1 diem) ChiJng minh rkng trong 10 só nguyen dúdng lien tiep khong ton
tai hai só c6 \i6c chung Idn hdn 9. , • f { i •^-r .^^ (A
Cfiu 5. (3,5 diem) Cho tam gidc ABC khong \k tam gi^c can, biet tam gi^c ABC
ngoai tiep diTdng tron (I). Goi D, E, F Ian lu-dt la c^c tiep diem cua BC, CA, AB vdi dirdng tron (I). Goi M la giao diem cua diTcfng thing EF v^ diT^ng
thing BC, biét AD dt diTcfng tr6n (I) tai diem N (N khong trung vdi D), goi