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6
2018 PUMaC Algebra A6
2018 PUMaC Algebra A6
Source:
November 25, 2018
PuMAC
algebra
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be non-zero real numbers that satisfy
1
a
b
c
+
1
a
+
1
c
=
1
b
\frac{1}{abc} + \frac{1}{a} + \frac{1}{c} = \frac{1}{b}
ab
c
1
+
a
1
+
c
1
=
b
1
. The expression
4
a
2
+
1
+
4
b
2
+
1
+
7
c
2
+
1
\frac{4}{a^2 + 1} + \frac{4}{b^2 + 1} + \frac{7}{c^2 + 1}
a
2
+
1
4
+
b
2
+
1
4
+
c
2
+
1
7
has a maximum value
M
M
M
. Find the sum of the numerator and denominator of the reduced form of
M
M
M
.
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