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India Pre-Regional Mathematical Olympiad
2017 India PRMO
2
2017 preRMO p2, a\sqrt{a}+b\sqrt{b}=183, a\sqrt{b}+b\sqrt{a} = 182
2017 preRMO p2, a\sqrt{a}+b\sqrt{b}=183, a\sqrt{b}+b\sqrt{a} = 182
Source:
August 9, 2019
system of equations
algebra
Problem Statement
Suppose
a
,
b
a, b
a
,
b
are positive real numbers such that
a
a
+
b
b
=
183
,
a
b
+
b
a
=
182
a\sqrt{a} + b\sqrt{b} = 183, a\sqrt{b} + b\sqrt{a} = 182
a
a
+
b
b
=
183
,
a
b
+
b
a
=
182
. Find
9
5
(
a
+
b
)
\frac95 (a + b)
5
9
(
a
+
b
)
.
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