Tài liệu bồi dưỡng Toán THCS
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71$82
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⇒
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b b c a a b c
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2
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2 2 2
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⇒
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a b 2 ab
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a c 2 ac
⇒
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Dh
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2 2 2
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#WXoY%ˆhDx
⇒
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3
a b c 3 abc
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3
2 2 2 2 2 2
a b c 3 a b c
⇒
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3
2 2 2 3 3 3
a b c a b c 9 a b c 9abc
? Dh
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3
3
1 a 1 b 1 c 1 abc
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1 a 1 b 1 c 1 a b c ab ac bc abc.
+ + ≥
3
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3
2 2 2
ab ac bc 3 a b c
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3
3
2 2 2
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1 a 1 b 1 c 1 3 abc 3 a b c abc 1 abc
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m m 1
a b a b b a
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b a b a a b
2 4 2
23
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2
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1
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1 a
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2
1
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1 a
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+
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1
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1995
a 1995 a 1
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a 1995a 1995 a 1995 1995a
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1995
1995 1995 1995 1995
1994 soá
a 1995 a 1994 a 1 1 1 1995 a 19 95a
{ Dh
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a 1 b b 1 c c 1 a 6abc
°
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a 1 b b 1 c c 1 a a a b b b c c c a
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6
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a a b b b c c c a 6 a b c 6abc
| D"$+{Dh
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÷
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°
≤ =
+
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a b
≤ =
+
2 2
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b c
≤ =
+
2 2
c c 1
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a c
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÷
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a b c 1 1 1 1
2 a b c
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°
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D"!=•{B!7=7•9QDh!=•≥IQ1!821=821•82
°
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= − + = − + + + −
x x 1 1 x 1 x y z 3
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2
4
x 1 x 1 y 1 z 1 4 x 1 y 1 z 1
24
&*
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2
4
y 4 x 1 y 1 z 1
3
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( )
( )
≥ − − −
2
4
z 4 x 1 y 1 z 1
⇒ !=•≥IQ1!821=821•82
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≥ − −
3
a 3 a b b c c
°
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3
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M D"$+{B$7+79Dh
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°
+
≥
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2
b c
bc
2
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2 2
2
b c 1 a
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2 2
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( )
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− = − − = − − − ≤ − = +
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2
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J/ 18$218+2182≥H$+
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/
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1 1 1
1 1 1 64
a b c
°
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+ = ≥
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2
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1
a a a
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2
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1
b b
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2
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1
c c
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1 1 1
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e D"!{={Dh
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1
x 3
x y y
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1
VT x y y 3 3
x y y x y y
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+
≥
+
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x 1
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x 1 1 2 x 1
J/
+
−
x 8
x 1
9
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− − −
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x 1 2 x 1 6
x 1 x 1 x 1
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a 1 4 2 4 a 1 4 a 1
⇔
+
≥
+
2
2
a 5
4
a 1
g Dh
+ +
+ + ≤ >
+ + +
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; a, b, c 0
a b b c c a 2
° <
+ ≥a b 2 ab
⇒
≤ =
+
ab ab ab
a b 2
2 ab
≤ =
+
bc bc bc
b c 2
2 bc
≤ =
+
ac ac ac
a c 2
2 ac
°
+ + ≥ + +
a b c ab bc ca
W$B"
+ + ≥ + +
2 2 2
a b c ab bc ca
°
+ + + +
+ + ≤ ≤
+ + +
ab bc ca ab bc ac a b c
a b b c c a 2 2
h Dh
+ ≤
+ +
2 2
4 4
x y 1
4
1 16x 1 16y
∀!=∈v
°
( )
= ≤ =
+
+
2 2 2
4 2 2
x x x 1
8
1 16x 2.4x
1 4x
25
