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South East Mathematical Olympiad
2018 South East Mathematical Olympiad
1
1
Part of
2018 South East Mathematical Olympiad
Problems
(1)
Find the range of c satisfying an inequality.
Source: 2018 China Southeast MO Grade 10 P1
7/30/2018
Assume
c
c
c
is a real number. If there exists
x
∈
[
1
,
2
]
x\in[1,2]
x
∈
[
1
,
2
]
such that
max
{
∣
x
+
c
x
∣
,
∣
x
+
c
x
+
2
∣
}
≥
5
\max\left\{\left |x+\frac cx\right |, \left |x+\frac cx + 2\right |\right\}\geq 5
max
{
x
+
x
c
,
x
+
x
c
+
2
}
≥
5
, please find the value range of
c
c
c
.
algebra
Inequality
inequalities