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Italian WinterCamp test07 problem3
Italian WinterCamp test07 problem3
Source:
January 29, 2007
inequalities
algebra
IMO Shortlist
Hi
Problem Statement
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are the sides of a triangle, prove that
b
+
c
−
a
b
+
c
−
a
+
c
+
a
−
b
c
+
a
−
b
+
a
+
b
−
c
a
+
b
−
c
≤
3
\frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}+\frac{\sqrt{c+a-b}}{\sqrt{c}+\sqrt{a}-\sqrt{b}}+\frac{\sqrt{a+b-c}}{\sqrt{a}+\sqrt{b}-\sqrt{c}}\leq 3
b
+
c
−
a
b
+
c
−
a
+
c
+
a
−
b
c
+
a
−
b
+
a
+
b
−
c
a
+
b
−
c
≤
3
Proposed by Hojoo Lee, Korea
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