M, D, E ,N thang hang ^ J,
b)Ap dung eau a:
a"* + b'* + c"* > âb^ + b^c^ + c^â > âbc + ab^c + abc^ = abe(a + b + c) Viabc < 0 a ^ + b H c ^ <a + b + c=> — + — + — <a + b + c a- b ' c-
abc be ca ab Bai 4: a) (1) va (2) c6: ac = -(m^ + l)(p^ + 2) < 0, Vm, n, p.
[(1) CO 2 nghiem trai dau x, > 0, X j < 0 (2) CO 2 nghiem trdi dafu X3 > 0, X4 < 0
b) Ta c6:xi>01a nghiem cua (1) =:> (m^ + l)x^ +nx, - p^ - 2 = 0
•'01 , Vm, n, p. , Vm, n, p. o p^ + 2 - nx, - (m^ + 1) xf = 0 o (p^ + 2) => X3 = — > 0 la nghiem cua (2) M V r 1 ^ - n - m - 1 = 0 v ^ i J
TiTdng tiT: X2 < 0 la nghiem ciia (1) X4 = — < 0 la nghiem cua (2)
* 2
Ap dung bát ding thuTc Co-si cho hai so di/dng, ta c6:
1 r o X| + X3 = X, + — > 2 ; (-X2) + (-X4) = (-X2) + > 2 X, I x j Lai CO: X1.X2.X3.X4 = X1.X2. — . — = 1 X, X2 1^ Do vay: Xi - X2 + X3 - X4 + X1.X2.X3.X4 > 5
Bai 5: a) Ta c6: BE va CF la hai difdng cao cua AABC B H 1 AC va C H 1 AB.
Luy§n .;„h ]• t'l/ac kl thi vSo Idp 10 ba mign B^c, Trung, Nam mOn Toi^n _ Nguygn Disc
Do do tỉ giac BHCK la hinh binh hanh
=> BH // CK vh CH // BK.
AC J. CK va AB 1 BK => ABK = ACK = 90"
=> A, B, C, K e difdng tron diTdng kinh AK. Ma A, B, C G (O) =^ K 6 (O).
Ta CO tu" giac BHCK la hinh binh hanh Hai di/dng cheo BC va HK cat nhau tai trung diem cua moi diTdng. ' > Ma I la trung diem cua BC
=> I cung la trung diem cua HK.
Lai CO AK la diTdng kinh cua (O) => O la U-ung diem cua AK
i=> 01 la diTdng trung binh cua AAHK => AH = 20L b) OB = OC => AOBC can tai O
=> di/dng trung tuyen 01 cung la difdng cao, phan giac. f O i l BC
• if!
IOC = ^BOC = a (khong đi do O, B, C co dinh) => OI = OC.cos IOC = Rcosa
Do do: SBHC = ^ BC.HD = ^ BC.(AD - AH) < i BC.(AI - 20I)
< ^ BC.(AO + 01 - 201) = ^ BC.(R - Rcosa) (khong doi) Dau"=" x a y r a o < D = I
A, O, I thing hang o A la diem chinh giiJa cung Idn BC. Vay khi A la diem chinh giffa cung Idn B C thi SBHC nhaft.
c) Ta c6: BHA, = ACB (cung phu CBEj BApH = ACB (cung chan AB)
ABHA, can tai B. => BHA, = BA|H
=> dúdng cao BD cung la di/dng trung tuyen TiTdng tir: HE = EB, va HP = PC,