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2017 JBMO Shortlist
A1
A1
Part of
2017 JBMO Shortlist
Problems
(1)
\sqrt{a^2+b^2+2}+\sqrt{b^2+c^2+2 }+\sqrt{c^2+a^2+2}\ge 6
Source: JBMO Shortlist 2017 A1
7/25/2018
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers such that
a
+
b
+
c
+
a
b
+
b
c
+
c
a
+
a
b
c
=
7
a + b + c + ab + bc + ca + abc = 7
a
+
b
+
c
+
ab
+
b
c
+
c
a
+
ab
c
=
7
. Prove that
a
2
+
b
2
+
2
+
b
2
+
c
2
+
2
+
c
2
+
a
2
+
2
≥
6
\sqrt{a^2 + b^2 + 2 }+\sqrt{b^2 + c^2 + 2 }+\sqrt{c^2 + a^2 + 2 } \ge 6
a
2
+
b
2
+
2
+
b
2
+
c
2
+
2
+
c
2
+
a
2
+
2
≥
6
.
algebra
Inequality
real number
3-variable inequality