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|ax+by|+ |bx + ay| = 2|x| + 2|y| 2013 Romania District VII p2
|ax+by|+ |bx + ay| = 2|x| + 2|y| 2013 Romania District VII p2
Source:
September 1, 2024
algebra
Problem Statement
Find all pairs of real numbers
(
a
,
b
)
(a, b)
(
a
,
b
)
such that the equality
∣
a
x
+
b
y
∣
+
∣
b
x
+
a
y
∣
=
2
∣
x
∣
+
2
∣
y
∣
|ax+by|+ |bx + ay| = 2|x| + 2|y|
∣
a
x
+
b
y
∣
+
∣
b
x
+
a
y
∣
=
2∣
x
∣
+
2∣
y
∣
holds for all reals
x
x
x
and
y
y
y
.
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