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Soros Olympiad in Mathematics
V Soros Olympiad 1998 - 99 (Russia)
11.5
min (x -y)^2 + (z - u)^2 (V Soros Olympiad 1998-99 Round 1 11.5)
min (x -y)^2 + (z - u)^2 (V Soros Olympiad 1998-99 Round 1 11.5)
Source:
May 25, 2024
algebra
inequalities
Problem Statement
Find the smallest value of the expression
(
x
−
y
)
2
+
(
z
−
u
)
2
,
(x -y)^2 + (z - u)^2,
(
x
−
y
)
2
+
(
z
−
u
)
2
,
if
(
x
−
1
)
2
+
(
y
−
4
)
2
+
(
z
−
3
)
2
+
(
u
−
2
)
2
=
1.
(x -1)^2 + (y -4)^2 + (z-3)^2 + (u-2)^2 = 1.
(
x
−
1
)
2
+
(
y
−
4
)
2
+
(
z
−
3
)
2
+
(
u
−
2
)
2
=
1.
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