I Do 66 khong c6 45 bi nao cung m^ụ Bai toan khong dung neu ta chi lay ra
b)Taco: O E= OC (AOB E= AODC) ACEF can tai C, CO la difdng cao
=> CO la diTdng trung triTc cua doan th^ng EF => OE = OF. Ta CO OE = OF = OC.
Vay O la lam dúdng tron ngoai tiép tam giac CEF. c) ACBD CO CI la diTdng phan giac (gt)
IB ID
BC CD IB.CD = ID.BC
Ta co: DAF = AEB (so le trong AD // BC) AEB - AFD (ACEF can tai C)
Nen DAF = AFD => ADAF can tai D => DF = DA = BC. M3t khac I thuoc difcJng trung triTc cua EF => EI = FI
Do do: IB.BẸEI = IB.AB.EI = IB.CD.EI = ID.BC.EI = ID.DF.FI
Nhan xet: Bai toan nay khong kho, chi can nhan ra cac tam giac can CEF, ABE, DAF la co diTdc IcJi giaị
Luypn giai 6i Uudc ki thi vAo I6p 10 ba mign B&c. Trung. Nam mOn Toan _ NguySn Pile iSn
Bai 4: Ta c6: 4ý(x - y)^ > 0 ^ 4 x y - 8xý + 4y^ > 0
=>x' + 8xý < x U 4x'ý + 4ý ^ x' + 8xý < (x' + 2y^f
_.4 .,4
x^ + 8xy^ ( x 2 + 2 y 2 ) ' V ^ ' + S y ' x^ + 2y (1) Mat khac, ta c6: (x - y)^(x^ + xy + 2y^) > 0
=> (x^ + 2y^ - 2xy - y^)(x^ + 2y^ + xy) > 0
(x' + ly^ + x'y + 2xý - 2x'y - 4xý - 2xV' - x'ý - 2ý - xý > 0
=> (x^ + 2ý)^ > 2ý' + x'y + 3\y + 3xý
=i> (x^ + 2y^)^ >y^ + y(ý + x' + Bx^ + 3xy^)
• (x' + 2ý)' > ý + y(x + y)' 4y^ 4y^
y ^ + y ( x + y f (x^+2y^) 4y^ 2ý Tiif(l) va (2) c6: P = (2) 4y-^ > 1 Dáu "=" x a y r a o o X = ỵ Vx^+8y3 ^ y ^ + ( x + y) 4 y 2( x - y) ' = 0 ( x - y) ^ ( x 2 +xy + 2y2) = 0 Vay gia tri nho nhat cua bieu thiJc P la 1.
Nh§n xet: Day la bai toan kho nhat cua de thi, mac du chung ta nhan ra r^ng dáu "=" xay ra <=> x = y va gia tri nho nhaft cua bieu thtfc P la I , nhifng de CO diTcfc Idi giai nhiT tren la khọ Cac ban hay thuT tim them cac each giai
khdc nifa nhẹ
, , D i s 6 6 5 \E THI TUYEN SINH VAO LdP 10 CHUYEN TOAN,
, ( TRl/CJNG THPT CHUYEN KHTN, DHKHTN, DHQG HA NQI NAM HOC 2011 - 2012
Bai 1: (3 diem)
a) Giai phUcfng trinh: ( V x + 3 - Vx)(Vl - x + l) = 1. b) Giai he phÚcJng trinh: x^ + y^ = 2x^y^ b) Giai he phÚcJng trinh: x^ + y^ = 2x^y^
(x + y ) ( l + xy) = 4x^y^
Bai 2: (2,5 diem)
a) V d i m o i so ihuTc a ta goi phan nguyen cua a la so nguyen Idn nhát khong viTdt qua a va k i hieu la [ a ] . ChiJng minh rang v d i m o i só nguyen dU'dng n,