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max of 4(sum a_i^3 )-(sum a_i^4) when sum a_i^2 <=12 (HOMC 2015 S Q15)
max of 4(sum a_i^3 )-(sum a_i^4) when sum a_i^2 <=12 (HOMC 2015 S Q15)
Source:
September 7, 2019
algebra
maximum
Summation
inequalities
Problem Statement
Let the numbers
a
,
b
,
c
a, b,c
a
,
b
,
c
satisfy the relation
a
2
+
b
2
+
c
2
+
d
2
≤
12
a^2+b^2+c^2+d^2 \le 12
a
2
+
b
2
+
c
2
+
d
2
≤
12
. Determine the maximum value of
M
=
4
(
a
3
+
b
3
+
c
3
+
d
3
)
−
(
a
4
+
b
4
+
c
4
+
d
4
)
M = 4(a^3 + b^3 + c^3+d^3) - (a^4 + b^4 + c^4+d^4)
M
=
4
(
a
3
+
b
3
+
c
3
+
d
3
)
−
(
a
4
+
b
4
+
c
4
+
d
4
)
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