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Mathematics
Mathematics
Problem
10. The ratio of the A.M. and G.M. of two positive numbers
a
a
a
and
b
b
b
, is
m
:
n
m: n
m
:
n
. Show that
a
:
b
=
(
m
+
m
2
−
n
2
)
:
(
m
−
m
2
−
n
2
)
a: b=\left(m+\sqrt{m^{2}-n^{2}}\right):\left(m-\sqrt{m^{2}-n^{2}}\right)
a
:
b
=
(
m
+
m
2
−
n
2
)
:
(
m
−
m
2
−
n
2
)
.
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