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National High School Mathematics League
2002 National High School Mathematics League
11
The Minumum Value
The Minumum Value
Source: 2002 National High School Mathematics League, Exam One, Problem 11
March 16, 2020
Problem Statement
If
log
4
(
x
+
2
y
)
+
log
4
(
x
−
2
y
)
=
1
\log_4 (x+2y)+\log_4 (x-2y)=1
lo
g
4
(
x
+
2
y
)
+
lo
g
4
(
x
−
2
y
)
=
1
, then the minumum value of
∣
x
∣
−
∣
y
∣
|x|-|y|
∣
x
∣
−
∣
y
∣
is________.
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