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Russia Contests
All-Russian Olympiad
1962 All-Soviet Union Olympiad
7
Inequality with 4 variable
Inequality with 4 variable
Source:
April 6, 2016
inequalities
Problem Statement
Let
a
;
b
;
c
;
d
>
0
a;b;c;d>0
a
;
b
;
c
;
d
>
0
such that
a
b
c
d
=
1
abcd=1
ab
c
d
=
1
. Prove that
a
2
+
b
2
+
c
2
+
d
2
+
a
(
b
+
c
)
+
b
(
c
+
d
)
+
c
(
d
+
a
)
≥
10
a^2+b^2+c^2+d^2+a(b+c)+b(c+d)+c(d+a)\ge 10
a
2
+
b
2
+
c
2
+
d
2
+
a
(
b
+
c
)
+
b
(
c
+
d
)
+
c
(
d
+
a
)
≥
10
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