MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
USAMO
1978 USAMO
1
1978 USAMO #1
1978 USAMO #1
Source:
August 16, 2011
AMC
USA(J)MO
USAMO
inequalities
vector
geometric sequence
Problem Statement
Given that
a
,
b
,
c
,
d
,
e
a,b,c,d,e
a
,
b
,
c
,
d
,
e
are real numbers such that
a
+
b
+
c
+
d
+
e
=
8
a+b+c+d+e=8
a
+
b
+
c
+
d
+
e
=
8
,
a
2
+
b
2
+
c
2
+
d
2
+
e
2
=
16
a^2+b^2+c^2+d^2+e^2=16
a
2
+
b
2
+
c
2
+
d
2
+
e
2
=
16
.Determine the maximum value of
e
e
e
.
Back to Problems
View on AoPS