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German National Olympiad
1963 German National Olympiad
3
3
Part of
1963 German National Olympiad
Problems
(1)
sum a^2/( b^2 + c^2 ) >=3/2
Source: 1962-63 Germany R4 12.3
10/12/2024
It has to be proven: If at least two of the real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
are different from zero, then the inequality holds
a
2
b
2
+
c
2
+
b
2
c
2
+
a
2
+
c
2
a
2
+
b
2
≥
3
2
\frac{a^2}{b^2 + c^2} + \frac{b^2}{c^2 + a^2} + \frac{c^2}{a^2 + b^2} \ge \frac32
b
2
+
c
2
a
2
+
c
2
+
a
2
b
2
+
a
2
+
b
2
c
2
≥
2
3
Under what conditions does equality occur?
algebra
inequalities