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National and Regional Contests
Kosovo Contests
Kosovo Team Selection Test
2019 Kosovo Team Selection Test
5
Kosovo TST 2019 P5
Kosovo TST 2019 P5
Source:
April 15, 2019
inequalities
algebra
Problem Statement
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
are fixed positive real numbers. Find the maximum value of the function
f
:
R
+
0
→
R
f: \mathbb{R^{+}}_{0} \rightarrow \mathbb{R}
f
:
R
+
0
→
R
f
(
x
)
=
a
+
b
x
b
+
c
x
+
b
+
c
x
c
+
d
x
+
c
+
d
x
d
+
a
x
+
d
+
a
x
a
+
b
x
,
x
≥
0
f(x)=\frac{a+bx}{b+cx}+\frac{b+cx}{c+dx}+\frac{c+dx}{d+ax}+\frac{d+ax}{a+bx}, x \geq 0
f
(
x
)
=
b
+
c
x
a
+
b
x
+
c
+
d
x
b
+
c
x
+
d
+
a
x
c
+
d
x
+
a
+
b
x
d
+
a
x
,
x
≥
0
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