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Dutch Mathematical Olympiad
2011 Dutch Mathematical Olympiad
4
4
Part of
2011 Dutch Mathematical Olympiad
Problems
(1)
2x2 system a\sqrt{a}+ b\sqrt{b} = 134 , a\sqrt{b}+ b\sqrt{a} = 126
Source: Dutch NMO 2011 p4
9/6/2019
Determine all pairs of positive real numbers
(
a
,
b
)
(a, b)
(
a
,
b
)
with
a
>
b
a > b
a
>
b
that satisfy the following equations:
a
a
+
b
b
=
134
a\sqrt{a}+ b\sqrt{b} = 134
a
a
+
b
b
=
134
and
a
b
+
b
a
=
126
a\sqrt{b}+ b\sqrt{a} = 126
a
b
+
b
a
=
126
.
algebra
system of equations
radical