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National and Regional Contests
Greece Contests
Greece JBMO TST
1998 Greece JBMO TST
1
Greece TST 1998 Q1
Greece TST 1998 Q1
Source:
March 11, 2013
inequalities unsolved
inequalities
Problem Statement
If
x
,
y
,
z
>
0
,
k
>
2
x,y,z > 0, k>2
x
,
y
,
z
>
0
,
k
>
2
and
a
=
x
+
k
y
+
k
z
,
b
=
k
x
+
y
+
k
z
,
c
=
k
x
+
k
y
+
z
a=x+ky+kz, b=kx+y+kz, c=kx+ky+z
a
=
x
+
k
y
+
k
z
,
b
=
k
x
+
y
+
k
z
,
c
=
k
x
+
k
y
+
z
, show that
x
a
+
y
b
+
z
c
≥
3
2
k
+
1
\frac{x}{a} + \frac{y}{b} + \frac{z}{c} \ge \frac{3}{2k+1}
a
x
+
b
y
+
c
z
≥
2
k
+
1
3
.
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