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2024 Indonesia TST
A
Absolute value, bash go brrr
Absolute value, bash go brrr
Source: Indonesia 2024 TSTST - Algebra
February 29, 2024
algebra
inequalities
Indonesia
Indonesia TST
absolute value
Problem Statement
Given real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
which satisfies
∣
x
+
y
+
z
∣
+
∣
x
y
+
y
z
+
z
x
∣
+
∣
x
y
z
∣
≤
1
|x+y+z|+|xy+yz+zx|+|xyz| \le 1
∣
x
+
y
+
z
∣
+
∣
x
y
+
yz
+
z
x
∣
+
∣
x
yz
∣
≤
1
Show that
m
a
x
{
∣
x
∣
,
∣
y
∣
,
∣
z
∣
}
≤
1
max\{ |x|,|y|,|z|\} \le 1
ma
x
{
∣
x
∣
,
∣
y
∣
,
∣
z
∣
}
≤
1
.
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