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Canada National Olympiad
2017 Canada National Olympiad
1
CMO 2017 P1
CMO 2017 P1
Source: Canadian Mathematical Olympiad
March 31, 2017
algebra
inequalities
Canada
Problem Statement
For pairwise distinct nonnegative reals
a
,
b
,
c
a,b,c
a
,
b
,
c
, prove that
a
2
(
b
−
c
)
2
+
b
2
(
c
−
a
)
2
+
c
2
(
b
−
a
)
2
>
2
\frac{a^2}{(b-c)^2}+\frac{b^2}{(c-a)^2}+\frac{c^2}{(b-a)^2}>2
(
b
−
c
)
2
a
2
+
(
c
−
a
)
2
b
2
+
(
b
−
a
)
2
c
2
>
2
.
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