MC vdi (O) (C la tiep diem) Ke CH vuong goc vdi AB (He AB), MB cat
c) Go iD la giaodi em cua CH va AB.
A A B C c6 A Q , BP Ik hai diTdng cao (AQ J . BC, BP 1 AC) c^t nhau tai H.
=> H la trifc tam cu a tam gidc A B C => C H 1 A B tai D => A D C = B D C = 90" X e t A A D C va AAPB c6 D A C (chung), A D C = APB ( = 90") ^
A D A C Do do A A D C ^ AAPB (g.g) — ^ ^ AP.AC = A B . A D Do do A A D C ^ AAPB (g.g) — ^ ^ AP.AC = A B . A D B D B C TiTdng tir A B D C A B Q A (g.g) => BQ.BC = A B . B D BQ A B Vay S = AP.AC + BQ.BC = A B . A D + A B . B D = A B ( A D + B D ) = A B . A B ^ • = 2R.2R = 4R^
N h a n x e t : Day cung 1^ bai todn quen thupc. Cau c) 1^ cau kho nhat cua bai toan nay, de c6 Idi giai cau c) can lam xuat hien diem D (la bai toan nang cao cua Idp 8).
Bai 5: b > — => Zx/b > 5 2 Vb - 5 > 0.
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A p dung bat d^ng thiJc Co-si cho hai so diTPng, ta c6 : + ( 2 V b- 5 ) > 2 J - ^ J — . ( 2 7 b- 5 )
2 V b- 5 V 2 V b- 5
a . ^ rr . ^ ^ r+ 2Vb - 5> 2 7 a o — a > 2 V a - 2 V b+ 5 (1)
2Vb - 5 2S-5
ChiJng minh tifdng tiT ta c6 : — > 2> / b- 2 V c+ 5 (2) 2Vc - 5
: ' ' - —f^.— >2y[c - 2yfa +5 (3)
2 V a- 5
Tir (1), (2), (3) c6 Q > 15. Dau " = " xay ra » a = b = c = 25 (thich hdp) Vay gi^ tri nho nhát cua Q la 15.
N h a n x e t: T i r b i e u t h i i ' c Q v k d i e u k i e n a , b, c > — o 2 7 a - 5 > 0 , 2 N / b - 5 > 0 ,
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2 Vc - 5 > 0 giup nghl den van dung bát d^ng thtfc Co-si cho hai so diTdng
n h i r d tren. Day la bai toan kho nhat cua de thi naỵ
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Cty TNHH MTV DWH Khang Vi$t
E ) ^ S O 21
DE THI TUYEN SINK LCiP 10 THPT, TJNH THANH HdA NAM HOC 2011 - 2012
Bai 1: (1.5 diem)
a) Cho hai so : b| = 1 + N/2 ; bj = 1 - ^/2. Tinh b, -f- bz. ' m + 2n = 1 m + 2n = 1
2m - n = - 3 b) Giai he phiTdng trinh :
Bai 2: (1,5 diem) Cho bieu thiJc: B = Vb Vb 4^lh - 1
b - 4
1
V b+ 2 vdi b > 0 va b ;t 4. , V b+ 2 V b- 2