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2019 Junior Balkan Team Selection Tests - Moldova
10
Moldova JTST 2019 P10
Moldova JTST 2019 P10
Source: Moldova JTST 2019
April 19, 2019
algebra
Moldova
Problem Statement
Positive real numbers
a
a
a
and
b
b
b
verify
a
5
+
b
5
=
a
3
+
b
3
a^5+b^5=a^3+b^3
a
5
+
b
5
=
a
3
+
b
3
. Find the greatest possible value of the expression
E
=
a
2
ā
a
b
+
b
2
E=a^2-ab+b^2
E
=
a
2
ā
ab
+
b
2
.
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