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Swedish Mathematical Competition
1978 Swedish Mathematical Competition
1
1
Part of
1978 Swedish Mathematical Competition
Problems
(1)
x^a + x^d>= x^b + x^c , for x>0 if a>b>c>d >= q 0 and a + d = b + c
Source: 1978 Swedish Mathematical Competition p1
3/26/2021
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be real numbers such that
a
>
b
>
c
>
d
≥
0
a>b>c>d\geq 0
a
>
b
>
c
>
d
≥
0
and
a
+
d
=
b
+
c
a + d = b + c
a
+
d
=
b
+
c
. Show that
x
a
+
x
d
≥
x
b
+
x
c
x^a + x^d \geq x^b + x^c
x
a
+
x
d
≥
x
b
+
x
c
for
x
>
0
x>0
x
>
0
.
inequalities
algebra