D B1 OB^ CH ± OBC HO =90 "
b) Chia kh6a la nhan hai ve phifdng trinh thiJ nhat vd i2 roi cpng vdi phiTOng trinh thiir hai, cho ta (x y + 2)^ = 0 cong vỉc nay cung rat quen thuoc do
trinh thiir hai, cho ta (x - y + 2)^ = 0 cong vỉc nay cung rat quen thuoc doi vdi hoc sinh gioi toan.
Cfiu 2. 2" + 1 = y ' o 2" = y ' - 1 « 2^ = (y + l)(y - D y + 1, y - 1 la cdc irdc tif nhien cua 2''
y + 1 = 2"^
Do do • y - 1 = 2" (vdi m, n e N va m > n) m + n = X
Nen 2"" - 2" = 2 (*)
• Neu n > 2 thi 2™ : 4 , 2" ':4 nen 2 " " - 2":4 c6n 2 / 4 . Khong xay ra tnfdng hdp nay
• Neu n = 1 thi 2"^ - 2 = 2 o 2"" = 4 » 2"" = 2^ o m = 2. Ta C O X = 3; y = 3 • Neu n = 0 thi 2™ - 1 = 2 o 2"" = 3; m g N. Khong xay ra triTdng hcJp nay
Vay nghiem tif nhien (x; y) la (3; 3).
NhSn x e t : Day la bai toan ve phiTdng trinh nghiem nguyen loai phi/dng trinh mu cung kha quen thuoc doi v d i hoc sinh gioi todn.
Cfiu 3. A p dung bat d^ng thufc Co-si cho hai so diTdng, ta c6
y V x X y z z ^ + j y > 2 1^ 1 1 1 - + - + - > 2 + M a i + -!- + - = l . D o d 6 J x y> 2 + ^ xy > 27xy + — Tf V 7 Z Z Cty TNHH MTV D W H Khang Vỉt
=> z + xy > z + 2 Jxy + — =>z + xy> y/z + ./-^ z [ y z
> V^ + ^ TTT^ > V^ + ^
Ti/cJng tir yjy + zx + ^J^^
A2 Va VxTyz > N/X + Vxyz Va VxTyz > N/X + Vxyz (1) (2) (3) 6r. Tii(l), (2). va (3), ta c6 V z T x y + V y + Z X + Vx + yz > ( 7 z + 7y + V x ) + Txyz li, s ' 1 1 O - + — + — ,z y y =^ + yz + Vy + zx + + xy > Txyz + Vx + 7y + Vz
N h a n x e t : Day la bai todn bat d i n g thiJc c6 dieu kien rang buoc. TO x, y, z >
0 thoa man 1 + 1 + 1 = 1 van dung bát d i n g thuTc Co-si cho hai so diTdng X y z
de diTdc: Vz + xy > Vz + that hay, sang taọ Ban doc hay tim them z
each giai khac cho bai toan naỵ
Cfiu 4. a) Ta c6 A D B = 9 0 " (G6c noi tiep ch^n nu-a diTdng tron) A H C = A D B ( = 90") C H // B D => A C F = A B D
M a A B D = A N F (Hai g6c npi tiep cung ch^n cung A D ) . Do d6 A C T = A N F
=> Tú giac A F C N npi tiep => FAC = FNC . M a D A E = D N E (Hai goc npi tiep cCing c h i n cung DE) va D A E = FAC (AE la tia phangidc D A B ) .
Do do FNC = D N E => Hai tia NC, NE trung nhaụ
Luyyn giai UB mux; m iiii vau wp m ua ""g'l rmngT-