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Rioplatense Mathematical Olympiad, Level 3
1993 Rioplatense Mathematical Olympiad, Level 3
4
4
Part of
1993 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
max of f(x,y) = \sqrt{(6 -x)(3 + y^2)} + \sqrt{(11 + x)(14 - y^2)}
Source: III - Rioplatense 1993 L3 P4
9/19/2022
x
x
x
and
y
y
y
are real numbers such that
6
−
x
6 -x
6
−
x
,
3
+
y
2
3 + y^2
3
+
y
2
,
11
+
x
11 + x
11
+
x
,
14
−
y
2
14 - y^2
14
−
y
2
are greater than zero. Find the maximum of the function
f
(
x
,
y
)
=
(
6
−
x
)
(
3
+
y
2
)
+
(
11
+
x
)
(
14
−
y
2
)
.
f(x,y) = \sqrt{(6 -x)(3 + y^2)} + \sqrt{(11 + x)(14 - y^2)}.
f
(
x
,
y
)
=
(
6
−
x
)
(
3
+
y
2
)
+
(
11
+
x
)
(
14
−
y
2
)
.
algebra
inequalities