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min x^2+y^2, x+y=2a-4, xy=a^2-3a+5 - 1988 Greece MO Grade XI p1
min x^2+y^2, x+y=2a-4, xy=a^2-3a+5 - 1988 Greece MO Grade XI p1
Source:
September 7, 2024
algebra
inequalities
Problem Statement
Given
x
,
y
,
a
∈
R
x,y,a\in \mathbb{R}
x
,
y
,
a
∈
R
,
x
+
y
=
2
a
−
4
x+y=2a-4
x
+
y
=
2
a
−
4
and
x
y
=
a
2
−
3
a
+
5
xy=a^2-3a+5
x
y
=
a
2
−
3
a
+
5
. What is the minimum value of
x
2
+
y
2
x^2+y^2
x
2
+
y
2
?
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