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2013 USAJMO
6
Square Root Equality
Square Root Equality
Source: 2013 USAJMO #6/USAMO #4
May 1, 2013
AMC
USA(J)MO
USAJMO
parameterization
inequalities
Problem Statement
Find all real numbers
x
,
y
,
z
≥
1
x,y,z\geq 1
x
,
y
,
z
≥
1
satisfying
min
(
x
+
x
y
z
,
y
+
x
y
z
,
z
+
x
y
z
)
=
x
−
1
+
y
−
1
+
z
−
1
.
\min(\sqrt{x+xyz},\sqrt{y+xyz},\sqrt{z+xyz})=\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}.
min
(
x
+
x
yz
,
y
+
x
yz
,
z
+
x
yz
)
=
x
−
1
+
y
−
1
+
z
−
1
.
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