A) A=( A+ B) (2≤ A + B) (2+ A− B)2=2A 2B 2+ ≤ . A) A=( A+ B)...
139. a)
A
=
(
a
+
b
) (
2
≤
a
+
b
) (
2
+
a
−
b
)
2
=
2a 2b 2
+
≤
.
=
= ⇔
⇔ = =
a
b
1
max A 2
a b
a b 1
2
+ =
b) Ta cĩ :
(
a
+
b
) (
4
≤
a
+
b
) (
4
+
a
−
b
)
4
=
2(a
2
+
b
2
+
6ab)
(
)
(
)
4
4
+
≤
+ +
+
≤
+ +
2
2
2
2
a
c
2(a
c
6ac) ;
a
d
2(a
d
6ad)
+
≤
+ +
+
≤
+
+
b
c
2(b
c
6bc) ;
b
d
2(b
d
6bd)
Tương tự :
(
)
4
2
2
+
≤
+
+
c
d
2(c
d
6cd)
Suy ra : B ≤ 6(a
2
+ b
2
+ c
2
+ d
2
+ 2ab + 2ac + 2ad + 2bc + 2bd + 2cd) = 6(a + b + c + d)
2
≤ 6
=
=
=
= ⇔
⇔ = = = =
1
a
b
c
d
max B 6
a b c d
+ + + =
a b c d 1
4
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