PHoNG GrAo DUC vA DAo rAo orpN euAu
on rnr cHeN Der rwfN D[/ THr Hec srNH crOr riNn
NAM HQC 2013-2014 M6n To6n - (Thdi gian ldm bdi 150 philt)
Bni 1.(5 tli6m)
)
);
)
2 Tim nghiQm nguy€n tti cria phuong trinh: x'-2y' :1
Bni 2 (s dicm)
1 Cho x > 0 Tim gi6 tri cria x eC UiCu thfc: M: ; l-, dat gi|tri lcnr
(x +2013)"
nh6t
@' 2.Cho a + b * c:0 Chrmg minh ratrg' ao +bo *c4 :I@ *n, +c2).
Bni 3 (s dicm)
it l Cho 3 s5 a,b,c th6a mdn tli0u kiQn: 01a,b,c <t .
v/
Chrmg minh r6ng: a, +b2 *c2 <l+azb*b2.c+c2a 2.Basti thgc a,b,c th6a mdn hQ thfc:
b+c < 0(1)
bc* ca> 0(2) Chrmg minh a,b,c ( 0.
< 0(3)
Bni 4 (s dicm)
l Cho tf.gi6c ABCD c6 AC
"at gO tpi O Ggi diQn tich cria cilc tarn gi6c AOB, COD lan luqt bdng S, vd S, , diQn tfch cria bl gi6c ABCD bdng S.
Aaa.rJ',t,
Uhrmg mrnh rdng: V^S > /S, +./E .
! 2 Cho ttuorJg trdn tdm O nOi ti6p trong mQt tam gi6c ABC vd ti6p xric v6i c6c
cAnh AC, BC 16n lugt tai M vd N C6c ducrng phan gi6c cta c6c g6c A, B ctra tam gi6c ABC cit dulng thdng MN lAn lugt tpi P vd Q.
Chrmg minh: MP.OA: BC.OQ
HCt