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Moldova Team Selection Test
2022 Moldova Team Selection Test
2
a^4+b^4+c^4+d^4+4(a+b+c+d)^2
a^4+b^4+c^4+d^4+4(a+b+c+d)^2
Source: Moldova TST 2022
April 1, 2022
inequalities
Problem Statement
Real numbers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
satisfy
a
2
+
b
2
+
c
2
+
d
2
=
4.
a^2+b^2+c^2+d^2=4.
a
2
+
b
2
+
c
2
+
d
2
=
4.
Find the greatest possible value of
E
(
a
,
b
,
c
,
d
)
=
a
4
+
b
4
+
c
4
+
d
4
+
4
(
a
+
b
+
c
+
d
)
2
.
E(a,b,c,d)=a^4+b^4+c^4+d^4+4(a+b+c+d)^2 .
E
(
a
,
b
,
c
,
d
)
=
a
4
+
b
4
+
c
4
+
d
4
+
4
(
a
+
b
+
c
+
d
)
2
.
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