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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2024 Korea Junior Math Olympiad (First Round)
12.
12.
Part of
2024 Korea Junior Math Olympiad (First Round)
Problems
(1)
Algebra Finding Maximum
Source: 2024 KJMO round 1
10/26/2024
For reals
x
,
y
x,y
x
,
y
, find the maximum of A.
A
=
−
x
2
−
y
2
−
2
x
y
+
30
x
+
30
y
+
75
3
x
2
−
12
x
y
+
12
y
2
+
12
A=\frac{-x^2-y^2-2xy+30x+30y+75}{3x^2-12xy+12y^2+12}
A
=
3
x
2
−
12
x
y
+
12
y
2
+
12
−
x
2
−
y
2
−
2
x
y
+
30
x
+
30
y
+
75
algebra
maximum value