MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2018 India PRMO
23
23
Part of
2018 India PRMO
Problems
(1)
Simple inequality
Source: 2018 PRMO (IMO selection Stage -1 in india)
9/29/2018
What is the largest positive integer
n
n
n
such that
a
2
b
29
+
c
31
+
b
2
c
29
+
a
31
+
c
2
a
29
+
b
31
≥
n
(
a
+
b
+
c
)
\frac{a^2}{\frac{b}{29} + \frac{c}{31}}+\frac{b^2}{\frac{c}{29} + \frac{a}{31}}+\frac{c^2}{\frac{a}{29} + \frac{b}{31}} \ge n(a+b+c)
29
b
+
31
c
a
2
+
29
c
+
31
a
b
2
+
29
a
+
31
b
c
2
≥
n
(
a
+
b
+
c
)
holds for all positive real numbers
a
,
b
,
c
a,b,c
a
,
b
,
c
.
inequalities
algebra