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2014 EGMO
1
1
Part of
2014 EGMO
Problems
(1)
If a,b,c are sides of triangle then so are are <a^2+bct>
Source: European Girls’ Mathematical Olympiad-2014 - DAY 1 - P1
4/12/2014
Determine all real constants
t
t
t
such that whenever
a
a
a
,
b
b
b
and
c
c
c
are the lengths of sides of a triangle, then so are
a
2
+
b
c
t
a^2+bct
a
2
+
b
c
t
,
b
2
+
c
a
t
b^2+cat
b
2
+
c
a
t
,
c
2
+
a
b
t
c^2+abt
c
2
+
ab
t
.
algebra
EGMO