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Problem 1
max{z} if x^2≥y+z & cyclic
max{z} if x^2≥y+z & cyclic
Source: S&M 2002 2nd Grade P1
May 14, 2021
inequalities
Problem Statement
Real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
satisfy the inequalities
x
2
≤
y
+
z
,
y
2
≤
z
+
x
z
2
≤
x
+
y
.
x^2\le y+z,\qquad y^2\le z+x\qquad z^2\le x+y.
x
2
≤
y
+
z
,
y
2
≤
z
+
x
z
2
≤
x
+
y
.
Find the minimum and maximum possible values of
z
z
z
.
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