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2023 MOAA
13
2023 MOAA Team P13
2023 MOAA Team P13
Source:
October 14, 2023
MOAA 2023
Problem Statement
If real numbers
x
x
x
,
y
y
y
, and
z
z
z
satisfy
x
2
−
y
z
=
1
x^2-yz = 1
x
2
−
yz
=
1
and
y
2
−
x
z
=
4
y^2-xz = 4
y
2
−
x
z
=
4
such that
∣
x
+
y
+
z
∣
|x+y+z|
∣
x
+
y
+
z
∣
is minimized, then
z
2
−
x
y
z^2-xy
z
2
−
x
y
can be expressed in the form
a
−
b
\sqrt{a}-b
a
−
b
where
a
a
a
and
b
b
b
are positive integers. Find
a
+
b
a+b
a
+
b
.Proposed by Andy Xu
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