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1983 Poland - Second Round
2
2
Part of
1983 Poland - Second Round
Problems
(1)
\sqrt{a+b-c}+\sqrt{a-b+c}+\sqrt{-a+b+c} \leq \sqrt{a}+\sqrt{b} + \sqrt{c}
Source: Polish MO Recond Round 1983 p2
9/9/2024
There are three non-negative numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
such that the sum of each two is not less than the remaining one. Prove that
a
+
b
−
c
+
a
−
b
+
c
+
−
a
+
b
+
c
≤
a
+
b
+
c
.
\sqrt{a+b-c} + \sqrt{a-b+c} + \sqrt{-a+b+c} \leq \sqrt{a} + \sqrt{b} + \sqrt{c}.
a
+
b
−
c
+
a
−
b
+
c
+
−
a
+
b
+
c
≤
a
+
b
+
c
.
algebra
inequalities