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max{a, b, c}>= 2, a+b+c=5, min{a^2+b^2+c^2} (HOMC 2008 J Q10)
max{a, b, c}>= 2, a+b+c=5, min{a^2+b^2+c^2} (HOMC 2008 J Q10)
Source:
July 25, 2019
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
∈
[
1
,
3
]
a,b,c \in [1, 3]
a
,
b
,
c
∈
[
1
,
3
]
and satisfy the following conditions:
m
a
x
{
a
,
b
,
c
}
≥
2
max \{a, b, c\}\ge 2
ma
x
{
a
,
b
,
c
}
≥
2
and
a
+
b
+
c
=
5
a + b + c = 5
a
+
b
+
c
=
5
What is the smallest possible value of
a
2
+
b
2
+
c
2
a^2 + b^2 + c^2
a
2
+
b
2
+
c
2
?
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