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1
Puerto Rico 2012 TST Problem 1
Puerto Rico 2012 TST Problem 1
Source:
April 26, 2012
inequalities
algebra proposed
algebra
Problem Statement
Let
x
,
y
x, y
x
,
y
and
z
z
z
be consecutive integers such that
1
x
+
1
y
+
1
z
>
1
45
.
\frac 1x+\frac 1y+\frac 1z >\frac{1}{45}.
x
1
+
y
1
+
z
1
>
45
1
.
Find the maximum value of
x
+
y
+
z
x + y + z
x
+
y
+
z
.
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