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Greece Junior Math Olympiad
2016 Greece Junior Math Olympiad
2
2
Part of
2016 Greece Junior Math Olympiad
Problems
(1)
Algebra equations
Source: Greece Archimedes Junior 2016
3/16/2020
Given is that
x
,
y
,
z
x, y, z
x
,
y
,
z
are real numbers, different from 0,
x
x
x
and
z
z
z
are different, such that
(
x
+
y
)
2
+
(
2
−
x
y
)
=
9
(x+y) ^2+(2-xy)=9
(
x
+
y
)
2
+
(
2
−
x
y
)
=
9
and
(
y
+
z
)
2
−
(
3
+
y
z
)
=
4
(y+z) ^2-(3+yz)=4
(
y
+
z
)
2
−
(
3
+
yz
)
=
4
Find the value of
A
=
(
x
/
y
+
y
2
/
x
2
+
z
3
/
x
2
y
)
(
y
/
z
+
z
2
/
y
2
+
x
3
/
y
2
z
)
(
z
/
x
+
x
2
/
z
2
+
y
3
/
z
2
x
)
=
?
A=(x/y+y^2/x^2+z^3/x^2y)(y/z+z^2/y^2+x^3/y^2z)(z/x+x^2/z^2+y^3/z^2x)=?
A
=
(
x
/
y
+
y
2
/
x
2
+
z
3
/
x
2
y
)
(
y
/
z
+
z
2
/
y
2
+
x
3
/
y
2
z
)
(
z
/
x
+
x
2
/
z
2
+
y
3
/
z
2
x
)
=
?
algebra