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5
SMT 2022 Algebra #5
SMT 2022 Algebra #5
Source:
March 27, 2023
inequalities
algebra
Problem Statement
x
x
x
,
y
y
y
, and
z
z
z
are real numbers such that
x
y
z
=
10
xyz=10
x
yz
=
10
. What is the maximum possible value of
x
3
y
3
z
3
−
3
x
4
−
12
y
2
−
12
z
4
x^3y^3z^3-3x^4-12y^2-12z^4
x
3
y
3
z
3
−
3
x
4
−
12
y
2
−
12
z
4
?
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