MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2015 India PRMO
17
PRMO 2015. p17.
PRMO 2015. p17.
Source:
April 9, 2024
algebra
Problem Statement
17.
17.
17.
Let
a
,
a,
a
,
b
,
b,
b
,
and
c
.
c.
c
.
be such that
a
+
b
+
c
=
0
a+b+c=0
a
+
b
+
c
=
0
and
P
=
a
2
2
a
2
+
b
c
+
b
2
2
b
2
+
c
a
+
c
2
2
c
2
+
a
b
P=\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ca}+\frac{c^2}{2c^2+ab}
P
=
2
a
2
+
b
c
a
2
+
2
b
2
+
c
a
b
2
+
2
c
2
+
ab
c
2
is defined. What is the value of
P
?
P ?
P
?
Back to Problems
View on AoPS