M, D, E ,N thang hang ^ J,
c) ChuTng minh cac dúdng tron ngoai tiep cac tam giac AHB ,B HC va AHC c6 ban kinh b^ng nhaụ
B a i 6: (1 diem) Cho tam giac A B C vuong tai Ạ Chufng minh r^ng: ACB A B AC + B C H U ( 5 N G D A N G I A I B a i 1: a) A = Vv-4V3 - ^Jl + 4^f3 = y]{2 - - ^/(2 + ^3)^ 2-N/ 3|-|2 + 73|=2 - V 3 - 2 - V 3= - 2 V 3 X y xy b) p =
i^^M^-^) (^^^M^^i) (V^ + i)(i - 77) ,.
x ( V ^ . i ) - y ( i- V 7) - x y ( s A^ . V 7 )
(V^ + V7)(V5^ + l)(l - ^/7)
XN/X + X - y + y^/y - xy(%/x + ^ y ) ^-
Luy§n giSi de tui'-i ki iin v , n i irip I d iịi [iiiSn B&c, Trung, Nam m6n ToAn _ Ngiiy8n Pile Ta'n
_ (Vx + V y ) ( x - Vxy + y) + (Vx + ^/y)(V5^ - V y ) - x y ( V ^ + V y )
_ (V^ + V y ) ( x - ^^^ + y + V ^ - V y - x y ) (V^ + V ^ ) ( V ^ + i ) ( i - V ^ )
_ + l ) - + l ) - y(x - 1 ) ^ + - ^/y - y>/^ + y) (V^ + i ) ( i - V 7 ) " (s/^ + i ) ( i - V^) „ ,
• P = 2 ihi Vx + Vxy - N/Y = 2 <=> Vx + ^xy - x/y - 1 = 1 o + V y ) - + 1 ) = 1 » (1 + V y ) ( ^ - 0 = 1 -1 y G Z =ị Vy e Z => N/X - 1 e U ( l ) = ± 1 • N e u V x - 1 = - 1 ^ Vx = 0 ^ x = 0=>Vy = - 2 ( v 6 1 i ) • N e u V x - 1 = 1 =^ ^/x = 2 = > x = 4=>^/y = 0 = > y = 0 T h ^ lai ta CO v d i X = 4 va y = 0 Ihi P = 2. Bai 2: a) m - 3 < 0 o m < 3. b) ( m - 3 ) . l + 2 + m = 1 = > m = 1.
c) De do thi cat 2 true toa dp: c^t Ox tai A(XA; 0) va c^t Oy tai B(0; ye) thi dieu kien m ^ 3. kien m ^ 3.
- ( 2 + m ) Thay toa dp diem A ta c6: (m - 3)XA + 2 + m = 0= > X A =
Thay toa dp diem B ta c6: ya = 2 + m
Ta CO tam giac O A B vuong tai O nen dien tich
m - 3 1 S = - O A . O B = - 2 2 YB yB = 6 o - ( 2 + m ) m - 3 = 3 .|2 + m|= 6 o - ( 2 + m ) m - 3 .(2 + m ) = 6 - ( 2 + m ) ' m - 3 = 6 TrUf/ng hi/p 1: ^ "^^ = 6 o - ( 2 + m)' = 6(m - 3) « m H 10m - 14 = 0 m- 3
Cty TNHH MTV DVVH Khang Vi$t
Á = 5^ - (-14) = 39 > 0 => m = - 5 ± N/39
TrUifng hcfp 2: - ( 2 + m ) '
= - 6 0 - ( 2 + m)^ = -6(m - 3) <=> - 2m + 22 = 0
m - 3
Á = ( - l ) ' - 2 2 = - 2 1 < O = > m = 0 Vay gia tri tim difpc: m = - 5 ± sfi9
Bai 3:
a) A = (2m + D ' - 4 ( m ' + m - 6) = 4 m ' + 4m + 1 - 4 m ' - 4m + 24 = 25 > 0 Phu"Png trinh CO hai nghiem phan biet: Phu"Png trinh CO hai nghiem phan biet:
2m + 1 + 5 ^ 2m + 1 - 5 ^ - ' * X| = = m + 3; x 2 = = m - 2
2 2 ' r^-'u • ^» ^ m + 3 < 0 r^-'u • ^» ^ m + 3 < 0
De hai nghiem deu am thi: < o < [m - 2 < 0
Nhan xet: Co the linh S = x, + X2; P = X|X2.
m < - 3
m < 2 <=> m < - 3 .
Dieu kien de P c6 2 nghiem deu am thi:
A > 0 I
S < 0 . Turdo tim diTpc m." r
P > 0 b) = 50 <o ( m + 3)-^ - ( m - 2)"^ = 0 b) = 50 <o ( m + 3)-^ - ( m - 2)"^ = 0 <=> <=> m"* + 9m^ + 27m + 27 - m"* + 6m^ - 12m + sl = 50 15m^ + 15m + 351=50 0 3m^ + 3m + 7 = 10 3m^ + 3m + 7 = 10 3 m ' + 3 m + 7 = - 1 0
Giai tCrng búdc hai phúcfng trinh tren: (1) o m = 3 m ^ + 3 m - 3 = 0 ( l ) 3m^ + 3 m + 17 = 0 ( 2 ) - 1 ± Vs Vay m = -\±S Co the tic |3m^ + 3m + 7|= 10 o 3 m + m + -2 7 3 = 10. ; (2) o m = 0
Nhan xet: m ' + m + - > 0, V m e M . N e n 3 m ' + 3m + 7 = 10 r o i giai phUPng trinh naỵ • j,<\
Bai 4:
X = (3b)' - 2.3b(3 + a) + 9 + 6a + a ' + á - 4a + 4 + 1997 = (3b)' - 2.3b(3 + a) + (3 + a ) ' + ( a ' - 4a + 4) + 1997 = (3b - 3 - a ) ' + (a - 2 ) ' + 1997 > 1997
Luy^n giai aj truflc kl t h i v^o I6p 10 ba miSn B^c, Tmng, Mam mOn Join _ N g u y j n Dijfc Tán
Dau " = " xay ra khi: 3b - 3 - a = 0 a - 2 = 0
3b - 3 - 2 = 0
a = 2 a = 2 3. Vay a = 2 va b = - thi X „ „ = 1997.
11 ., '
B a i 5: a) V i H ' doi xvfng vcfi H qua AC nen:
A H = A H ' , C H = CH', AC canh chung ^ A A H C = AAH'C (c.c.c)
b) B I ? C = 1 8 0 " - ( B^ + q + C ^ + C^) B A C = 1 8 0 " - (B^ + BJ + q + C^) B A C = 1 8 0 " - (B^ + BJ + q + C^)
Ma BJ = C^ (goc CO canh tiTdng uTng vuong goc)
C^ = C^ (do A A H C = AAH'C)=:> BJ = C^
Vay B T T C = B A C ma A , H ke nhau cung nhin doan BC. Nen A B C H ' cung n^m Iren diTdng tron (0;R).