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MBMT Guts Rounds
2015.16
2015.16
Part of
MBMT Guts Rounds
Problems
(1)
MBMT Guts #16
Source:
3/29/2015
Your math teacher asks you to rationalize the denominator of the expression
a
b
+
c
\frac{a}{b + \sqrt{c}}
b
+
c
a
, where
a
a
a
,
b
b
b
, and
c
c
c
are integers and
c
c
c
is not divisible by the square of any prime. You find that
a
b
+
c
\frac{a}{b + \sqrt{c}}
b
+
c
a
is equal to
30
−
5
14
11
\frac{30 - 5\sqrt{14}}{11}
11
30
−
5
14
. Compute the triple
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
.