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Bogdan Stan
2012 Bogdan Stan
1
a²+b²+c²<=2
a²+b²+c²<=2
Source: G.M. 10/2011
November 25, 2019
inequalities
algebra
Problem Statement
Let be three real numbers
a
,
b
,
c
∈
[
0
,
1
]
a,b,c\in [0,1]
a
,
b
,
c
∈
[
0
,
1
]
satisfying the condition
a
b
+
b
c
+
c
a
=
1.
ab+bc+ca=1.
ab
+
b
c
+
c
a
=
1.
Prove that
a
2
+
b
2
+
c
2
≤
2
,
a^2+b^2+c^2\le 2,
a
2
+
b
2
+
c
2
≤
2
,
and determine the cases in which equality is attained.
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