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Switzerland Contests
Switzerland Team Selection Test
2001 Switzerland Team Selection Test
2
2
Part of
2001 Switzerland Team Selection Test
Problems
(1)
\sqrt{a+b-c}+\sqrt{c+a-b}+\sqrt{b+c-a } \le \sqrt{a}+\sqrt{b}+\sqrt{c}
Source: Switzerland - Swiss TST 2001 p2
2/18/2020
If
a
,
b
a,b
a
,
b
, and
c
c
c
are the sides of a triangle, prove the inequality
a
+
b
−
c
+
c
+
a
−
b
+
b
+
c
−
a
≤
a
+
b
+
c
\sqrt{a+b-c}+\sqrt{c+a-b}+\sqrt{b+c-a } \le \sqrt{a}+\sqrt{b}+\sqrt{c}
a
+
b
−
c
+
c
+
a
−
b
+
b
+
c
−
a
≤
a
+
b
+
c
. When does equality occur?
inequalities
Geometric Inequalities