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Contest of the Centers of Excellency of Suceava
2012 Centers of Excellency of Suceava
1
Prove that (function)
Prove that (function)
Source:
March 31, 2013
function
induction
algebra unsolved
algebra
Problem Statement
Function
f
:
[
0
,
+
∞
)
→
[
0
,
+
∞
)
{{f\colon \mathbb[0, +\infty)}\to\mathbb[0, +\infty)}
f
:
[
0
,
+
∞
)
→
[
0
,
+
∞
)
satisfies the condition
f
(
x
)
+
f
(
y
)
≥
2
f
(
x
+
y
)
f(x)+f(y){\ge}2f(x+y)
f
(
x
)
+
f
(
y
)
≥
2
f
(
x
+
y
)
for all
x
,
y
≥
0
x,y{\ge}0
x
,
y
≥
0
. Prove that
f
(
x
)
+
f
(
y
)
+
f
(
z
)
≥
3
f
(
x
+
y
+
z
)
f(x)+f(y)+f(z){\ge}3f(x+y+z)
f
(
x
)
+
f
(
y
)
+
f
(
z
)
≥
3
f
(
x
+
y
+
z
)
for all
x
,
y
,
z
≥
0
x,y,z{\ge}0
x
,
y
,
z
≥
0
. Mathematical induction? __________________________________ Azerbaijan Land of the Fire :lol:
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