MathDB
Problems
Contests
National and Regional Contests
Korea Contests
Korea National Olympiad
2011 Korea National Olympiad
3
Korea Second Round 2011
Korea Second Round 2011
Source: Korea Second Round 2011 #3
August 21, 2011
algebra
polynomial
function
inequalities unsolved
inequalities
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
real numbers such that
a
+
b
+
c
+
d
=
19
a+b+c+d=19
a
+
b
+
c
+
d
=
19
and
a
2
+
b
2
+
c
2
+
d
2
=
91
a^2+b^2+c^2+d^2=91
a
2
+
b
2
+
c
2
+
d
2
=
91
. Find the maximum value of
1
a
+
1
b
+
1
c
+
1
d
\frac{1}{a} +\frac{1}{b} +\frac{1}{c} +\frac{1}{d}
a
1
+
b
1
+
c
1
+
d
1
Back to Problems
View on AoPS