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Nordic
1987 Nordic
4
4
Part of
1987 Nordic
Problems
(1)
a/b + b/c + c/a <= a^2/b^2 + b^2/c^2 + c^2/a^2
Source: Nordic Mathematical Contest 1987 #4
10/5/2017
Let
a
,
b
a, b
a
,
b
, and
c
c
c
be positive real numbers. Prove:
a
b
+
b
c
+
c
a
≤
a
2
b
2
+
b
2
c
2
+
c
2
a
2
\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a}\le \frac{a^2}{b^2} + \frac{b^2}{c^2} + \frac{c^2}{a^2}
b
a
+
c
b
+
a
c
≤
b
2
a
2
+
c
2
b
2
+
a
2
c
2
.
inequalities
algebra
High school olympiad