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National and Regional Contests
Moldova Contests
JBMO TST - Moldova
2010 Junior Balkan Team Selection Tests - Moldova
2
2
Part of
2010 Junior Balkan Team Selection Tests - Moldova
Problems
(1)
E= |(x-y)/(x+y)+(x^2-y^2)/(x^2+y^2)+(x^3-y^3)/(x^3+y^3)| if x + y = 3 \sqrt{xy
Source: 2010 Moldova JBMO TST p2
2/25/2021
The positive real numbers
x
x
x
and
y
y
y
satisfy the relation
x
+
y
=
3
x
y
x + y = 3 \sqrt{xy}
x
+
y
=
3
x
y
. Find the value of the numerical expression
E
=
∣
x
−
y
x
+
y
+
x
2
−
y
2
x
2
+
y
2
+
x
3
−
y
3
x
3
+
y
3
∣
.
E=\left| \frac{x-y}{x+y}+\frac{x^2-y^2}{x^2+y^2}+\frac{x^3-y^3}{x^3+y^3}\right|.
E
=
x
+
y
x
−
y
+
x
2
+
y
2
x
2
−
y
2
+
x
3
+
y
3
x
3
−
y
3
.
algebra