MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
JBMO TST - Turkey
2021 JBMO TST - Turkey
4
4
Part of
2021 JBMO TST - Turkey
Problems
(1)
Find the maximum value of x^3+2y
Source: 2021 Turkey JBMO TST P4
5/23/2021
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be real numbers such that
∣
y
z
−
x
z
∣
≤
1
and
∣
y
z
+
x
z
∣
≤
1
\left|\dfrac yz-xz\right|\leq 1\text{ and }\left|yz+\dfrac xz\right|\leq 1
z
y
−
x
z
≤
1
and
yz
+
z
x
≤
1
Find the maximum value of the expression
x
3
+
2
y
x^3+2y
x
3
+
2
y
inequalities
2-variable inequality
algebra
Turkey