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Saint Petersburg Mathematical Olympiad
2018 Saint Petersburg Mathematical Olympiad
6
inequalities
inequalities
Source: St. Petersburg Mathematical Olympiad 2018 P5
April 26, 2018
algebra
inequalities
Saint Petersburg
Problem Statement
Let
a
,
b
,
c
,
d
>
0
a,b,c,d>0
a
,
b
,
c
,
d
>
0
. Prove that
a
4
+
b
4
+
c
4
+
d
4
≥
4
a
b
c
d
+
4
(
a
−
b
)
2
a
b
c
d
a^4+b^4+c^4+d^4 \geq 4abcd+4(a-b)^2 \sqrt{abcd}
a
4
+
b
4
+
c
4
+
d
4
≥
4
ab
c
d
+
4
(
a
−
b
)
2
ab
c
d
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