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Junior Balkan MO
2000 Junior Balkan MO
1
Prove that x+y=10
Prove that x+y=10
Source:
October 4, 2005
quadratics
algebra
quadratic formula
Problem Statement
Let
x
x
x
and
y
y
y
be positive reals such that
x
3
+
y
3
+
(
x
+
y
)
3
+
30
x
y
=
2000.
x^3 + y^3 + (x + y)^3 + 30xy = 2000.
x
3
+
y
3
+
(
x
+
y
)
3
+
30
x
y
=
2000.
Show that
x
+
y
=
10
x + y = 10
x
+
y
=
10
.
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