D thing hang.
2) TaCO QT P= QAP fcM N] Tỉ gidc TQPA npi tiep AQ P= ATP Ma ATP = ABC (He qua goc npi tiep)
Suy ra AQP = ABC . Do do QS // BC // MN => ASQ = AMN Ma AMN + ARQ = 180" (TiJ giac RAMN npi tiep).
< X , < ... < X n •
Do do ASQ + ARQ = 180". Vay tú giac ARQS npi tiep. Do vay A, R, Q, S cung thupc mot difdng tr6n.
Nhan xet: Day la bai toan hinh hpc dẹ
Cau IV. Gia sur cac so cua tap hdp X diTpc s^p theo thu" tif x,
Ta CO x, + X2 < X, + Xj < ... < X| + x„ < X2 + x„. Doi vdi mot tap n so thiTc
phan biet bat ki, ta luon c6 it nhat (n - 1) + (n - 2) = 2n - 3 gia tri phan biet
cua cac tdng X| + Xj. Vay C(X) > 2n - 3.
Xet tap X, = {1,2,...,n}, ta c6 vdi mpi 1 < i < j < n thi
Xi + X: = i + j e {3,4 2n - 1) =^ C(X) = 2n - 3 . Vay minC(X) = 2 n - 3 . Vay minC(X) = 2 n - 3 .
So cac tdng x, + Xj (1 < i < j < n) b^ng " , suy ra C(X) < £^!Llil.
Cty TNHH MIV DWH Khang Vi^t
X^ttap = {2,2^ 2"}, thi vdi mpi l < i < j < n
• . C - Jạ ,ts;:c. • ni\t if '< .
Xj + Xj 2 + 2'
Gia sijr ton tai 1 < r < s < n sao cho x^ + x^ = Xj + Xj o 2*^ + 2^* = 2' + 2^ 2^:2* <::>2'(1 + 2'~') = 2'(1 + 2J"') => r = i => s = j => C(X2) = 2': 2 ' n(n -1) ' c — " • . , Vay maxC(X) = n(n -1 )
Nh§n xet: Day la b^i todn ve to hdp, bai todn n^y kh6 doi vdi cic hoc sinh
bSc THCS. xl - ^
D £ S 6 4 5
THI TUY^N S I N H VAO Ll3P 1 0 C H U Y E N TINH DfiNG NAI NAM HOC 2 0 1 2 - 2 0 1 3
Cfiu 1. (2,5 diem)
1) Giai cac phiTdng trinh > a) x^ - x^ - 20 = 0 b) Vx + 1 = X - 1
2) Giai he phiTdng trinh:
y - ^ 1
| y - 3 | = l x| = 3
Cfiu 2. (2,0 diem) Cho parabol y = x^ (P) va diTdng thing y = mx (d), vdi m la
tham so ^ j •
1) Tim cac gia tri cua m de (P) v^ (d) c^t nhau tai diem c6 tung dp b^ng 9. 2) Tim cac gia tri cua m de (P) va (d) c^t nhau tai 2 diem, ma khoang each giifa
hai diem n^y b^ng \/6 Cfiu 3. (2,0 diem)
1) Tinh: P - V 3 - 1
^ - S 2 + Sh-S
2) Chu-ng minh: â + b^ > ấb^ + â + b \t r^ng a + b > 0.
Cfiu 4. (3,5 diem) Cho tarn giac ABC vuong d A, diTdng cao AH. Ve diTdng tr6n lam O, dirdng kinh AH, diTdng tr6n nay c^t cac canh AB, AC theo ihiJ tiT tai Dva Ẹ
Luy$n gi^i 6i triiOc ki thi vao Idp 10 ba mjgn BJc, Tnjng. Nam iiiQii lujii _ r\ijuy5ii DJc Ifln