giotdang_kcd
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MiT Se CH? VI?T T?T
VA CAC KI HI?U TRONG LU?N VAN 7
1 MiT Se KI?N TH?C CO B?N 8
1.1 Cac kiAn thuc co ban . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.1 D?nh nghia va tEnh chat co ban cia bat dflng thuc . . . . . . . . . . . 8
1.1.2 MUt sL hEng dflng thuc thu?ng su d?ng. . . . . . . . . . . . . . . . . . 9
1.1.3 Bat dflng thuc AM O GM . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.4 Bat dflng thuc hoan v? . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.5 Bat dflng thuc Schur tEng quat . . . . . . . . . . . . . . . . . . . . . . 11
1.2 MUt sL k? neng chung minh bat dflng thuc co ban . . . . . . . . . . . . . . . 12
1.2.1 K? neng 1: Su d?ng tham sL khi biAn dEi. . . . . . . . . . . . . . . . . 12
1.2.2 K? neng 2: Su d?ng bat dflng thuc Cauchy O Schwarz. . . . . . . . . . 15
1.2.3 K? neng 3: K? thuOt thom h/ng tu. . . . . . . . . . . . . . . . . . . . 19
1.2.4 K? neng 4: Su d?ng bat dflng thuc ph?. . . . . . . . . . . . . . . . . . 24
1.2.5 K? neng 5: ChuyOn mUt biAn tr? thanh tham sL. . . . . . . . . . . . . 25
1.2.6 K? neng 6: Ch?n chiOu don gian tl bat dflng thuc d/ng phan thuc. . . 27
1.2.7 K? neng 7: Su d?ng hEng dflng thuc thEch hup. . . . . . . . . . . . . . 28
2 MiT Se PHUONG PHAP LAM M?NH B?T D?NG TH?C 32
2.1 Xay d?ng bat dflng thuc xoay vang tl bat dflng thuc
1
1 + x1
+
1
1 + x2
+ ::: +
1
1 + xn
=
n
1 + pn x1:x2:::xn
: . . . . . . . . . . . . . . . 32
2.2 Xay d?ng bat dflng thuc tl d/ng lam m/nh
a(a - b)2 = 0; a = 0: . . . . . . . . . . . . . . . . . . . . . . 37
2.3 Xay d?ng bat dflng thuc tl d/ng lam m/nh
(c - a) a +1 b - c +1 b = (a +(cb-) (ac)+2 b); a; b; c > 0: . . . . . . . . . . . . . . 44
2.4 Xay d?ng bat dflng thuc tl dflng thuc cia ham sL
y =
a:x + b
c:x + d . . . . . . . . . . . . . . . . . . . . . . . . 54
2.5 Xay d?ng bat dflng thuc lam m/nh nh? su d?ng bat dflng thuc Cauchy O
Schwarz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
MiT Se NH?N XET V? B?T D?NG TH?C D?NG PHAN TH?C 63
K?T LU?N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
TAI LI?U THAM KH?O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
K?T LU?N
LuOn ven da d/t duuc mUt sL kAt qua sau:
1. LuOn ven trAnh bay mUt sL bai toan va phuong phap giai bat dflng thuc co ban va
mUt sL bat dflng thuc trong cac dO thi toan quLc tA su d?ng cac bat dflng thuc tron.
2. LuOn ven da dua ra mUt sL phuong phap xay d?ng bat dflng thuc tl viUc lam m/nh
cac bat dflng thuc co ban.
3. LuOn ven gi?i thiUu mUt sL bat dflng thuc trong cac dO thi h?c quLc gia va quLc tA,
va cach suy luOn m? rUng cac bat dflng thuc tron.
4. LuOn ven tEng kAt mUt sL phuong phap thu?ng su d?ng khi chung minh bat dflng
thuc d/ng phan thuc.
Tl kAt qua cia luOn ven nay, ta thay rEng tl cac suy luOn don gian, loogic ta co thO
xay d?ng duuc mUt l?p cac bat dflng thuc hay va l/. Tac gia hy v?ng v?i y tu?ng tron sA giup
cho dUc gia xay d?ng duuc nhiOu bat dflng thuc khac lam phong phu thom cac bai toan bat
dflng thuc vLn da rat da d/ng.
Tac gia rat mong nhOn duuc s? gop y kiAn cia cac thAy co va cac d?ng nghiUp dO dO
tai nay tiAp t?c duuc hoan thiUn.
Tac gia xin chan thanh cam on!
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Password giải nén nếu cần: ket-noi.com | Bấm trực tiếp vào Link để tải:
MiT Se CH? VI?T T?T
VA CAC KI HI?U TRONG LU?N VAN 7
1 MiT Se KI?N TH?C CO B?N 8
1.1 Cac kiAn thuc co ban . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.1 D?nh nghia va tEnh chat co ban cia bat dflng thuc . . . . . . . . . . . 8
1.1.2 MUt sL hEng dflng thuc thu?ng su d?ng. . . . . . . . . . . . . . . . . . 9
1.1.3 Bat dflng thuc AM O GM . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.4 Bat dflng thuc hoan v? . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.1.5 Bat dflng thuc Schur tEng quat . . . . . . . . . . . . . . . . . . . . . . 11
1.2 MUt sL k? neng chung minh bat dflng thuc co ban . . . . . . . . . . . . . . . 12
1.2.1 K? neng 1: Su d?ng tham sL khi biAn dEi. . . . . . . . . . . . . . . . . 12
1.2.2 K? neng 2: Su d?ng bat dflng thuc Cauchy O Schwarz. . . . . . . . . . 15
1.2.3 K? neng 3: K? thuOt thom h/ng tu. . . . . . . . . . . . . . . . . . . . 19
1.2.4 K? neng 4: Su d?ng bat dflng thuc ph?. . . . . . . . . . . . . . . . . . 24
1.2.5 K? neng 5: ChuyOn mUt biAn tr? thanh tham sL. . . . . . . . . . . . . 25
1.2.6 K? neng 6: Ch?n chiOu don gian tl bat dflng thuc d/ng phan thuc. . . 27
1.2.7 K? neng 7: Su d?ng hEng dflng thuc thEch hup. . . . . . . . . . . . . . 28
2 MiT Se PHUONG PHAP LAM M?NH B?T D?NG TH?C 32
2.1 Xay d?ng bat dflng thuc xoay vang tl bat dflng thuc
1
1 + x1
+
1
1 + x2
+ ::: +
1
1 + xn
=
n
1 + pn x1:x2:::xn
: . . . . . . . . . . . . . . . 32
2.2 Xay d?ng bat dflng thuc tl d/ng lam m/nh
a(a - b)2 = 0; a = 0: . . . . . . . . . . . . . . . . . . . . . . 37
2.3 Xay d?ng bat dflng thuc tl d/ng lam m/nh
(c - a) a +1 b - c +1 b = (a +(cb-) (ac)+2 b); a; b; c > 0: . . . . . . . . . . . . . . 44
2.4 Xay d?ng bat dflng thuc tl dflng thuc cia ham sL
y =
a:x + b
c:x + d . . . . . . . . . . . . . . . . . . . . . . . . 54
2.5 Xay d?ng bat dflng thuc lam m/nh nh? su d?ng bat dflng thuc Cauchy O
Schwarz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
MiT Se NH?N XET V? B?T D?NG TH?C D?NG PHAN TH?C 63
K?T LU?N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
TAI LI?U THAM KH?O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
K?T LU?N
LuOn ven da d/t duuc mUt sL kAt qua sau:
1. LuOn ven trAnh bay mUt sL bai toan va phuong phap giai bat dflng thuc co ban va
mUt sL bat dflng thuc trong cac dO thi toan quLc tA su d?ng cac bat dflng thuc tron.
2. LuOn ven da dua ra mUt sL phuong phap xay d?ng bat dflng thuc tl viUc lam m/nh
cac bat dflng thuc co ban.
3. LuOn ven gi?i thiUu mUt sL bat dflng thuc trong cac dO thi h?c quLc gia va quLc tA,
va cach suy luOn m? rUng cac bat dflng thuc tron.
4. LuOn ven tEng kAt mUt sL phuong phap thu?ng su d?ng khi chung minh bat dflng
thuc d/ng phan thuc.
Tl kAt qua cia luOn ven nay, ta thay rEng tl cac suy luOn don gian, loogic ta co thO
xay d?ng duuc mUt l?p cac bat dflng thuc hay va l/. Tac gia hy v?ng v?i y tu?ng tron sA giup
cho dUc gia xay d?ng duuc nhiOu bat dflng thuc khac lam phong phu thom cac bai toan bat
dflng thuc vLn da rat da d/ng.
Tac gia rat mong nhOn duuc s? gop y kiAn cia cac thAy co va cac d?ng nghiUp dO dO
tai nay tiAp t?c duuc hoan thiUn.
Tac gia xin chan thanh cam on!
Do Drive thay đổi chính sách, nên một số link cũ yêu cầu duyệt download. các bạn chỉ cần làm theo hướng dẫn.
Password giải nén nếu cần: ket-noi.com | Bấm trực tiếp vào Link để tải:
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