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South East Mathematical Olympiad
2020 South East Mathematical Olympiad
1
China South East Mathematical Olympiad 2020 Grade10 Q1
China South East Mathematical Olympiad 2020 Grade10 Q1
Source: China Zhuji
August 5, 2020
inequalities
China
algebra
Problem Statement
Let
f
(
x
)
=
a
(
3
a
+
2
c
)
x
2
−
2
b
(
2
a
+
c
)
x
+
b
2
+
(
c
+
a
)
2
f(x)=a(3a+2c)x^2-2b(2a+c)x+b^2+(c+a)^2
f
(
x
)
=
a
(
3
a
+
2
c
)
x
2
−
2
b
(
2
a
+
c
)
x
+
b
2
+
(
c
+
a
)
2
(
a
,
b
,
c
∈
R
,
a
(
3
a
+
2
c
)
≠
0
)
.
(a,b,c\in R, a(3a+2c)\neq 0).
(
a
,
b
,
c
∈
R
,
a
(
3
a
+
2
c
)
=
0
)
.
If
f
(
x
)
≤
1
f(x)\leq 1
f
(
x
)
≤
1
for any real
x
x
x
, find the maximum of
∣
a
b
∣
.
|ab|.
∣
ab
∣.
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