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Korea Junior Mathematics Olympiad
2024 Korea Junior Math Olympiad (First Round)
12.
Algebra Finding Maximum
Algebra Finding Maximum
Source: 2024 KJMO round 1
October 26, 2024
algebra
maximum value
Problem Statement
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
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