MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2017 India PRMO
2
2
Part of
2017 India PRMO
Problems
(1)
2017 preRMO p2, a\sqrt{a}+b\sqrt{b}=183, a\sqrt{b}+b\sqrt{a} = 182
Source:
8/9/2019
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
)
.
system of equations
algebra