MathDB
Problems
Contests
National and Regional Contests
Serbia Contests
Serbia JBMO TST
2014 Serbia JBMO TST
1
1
Part of
2014 Serbia JBMO TST
Problems
(1)
Inequality
Source: Serbia JBMO TST 2014
4/15/2020
For
a
,
b
,
c
,
d
,
e
a, b, c, d, e
a
,
b
,
c
,
d
,
e
in the interval
[
0
,
1
]
[0,1]
[
0
,
1
]
, prove that
(
1
+
a
+
b
+
c
+
d
+
e
)
2
=
>
4
(
a
2
+
b
2
+
c
2
+
d
2
+
e
2
)
(1+a+b+c+d+e)^2=>4(a^2+b^2+c^2+d^2+e^2)
(
1
+
a
+
b
+
c
+
d
+
e
)
2
=>
4
(
a
2
+
b
2
+
c
2
+
d
2
+
e
2
)
inequalities