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max of 4(Σ a_i^3 )-(Σa_i^4) when Σa_i^2 <=8 (HOMC 2015 J Q15)
max of 4(Σ a_i^3 )-(Σa_i^4) when Σa_i^2 <=8 (HOMC 2015 J Q15)
Source:
August 6, 2019
maximum
inequalities
algebra
Problem Statement
Let the numbers
a
,
b
,
c
a, b,c
a
,
b
,
c
satisfy the relation
a
2
+
b
2
+
c
2
≤
8
a^2+b^2+c^2 \le 8
a
2
+
b
2
+
c
2
≤
8
. Determine the maximum value of
M
=
4
(
a
3
+
b
3
+
c
3
)
−
(
a
4
+
b
4
+
c
4
)
M = 4(a^3 + b^3 + c^3) - (a^4 + b^4 + c^4)
M
=
4
(
a
3
+
b
3
+
c
3
)
−
(
a
4
+
b
4
+
c
4
)
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