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2018 PUMaC Algebra A4
2018 PUMaC Algebra A4
Source:
November 25, 2018
PuMAC
algebra
Problem Statement
Suppose real numbers
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
satisfy
a
+
b
+
c
+
d
=
17
a + b + c + d = 17
a
+
b
+
c
+
d
=
17
and
a
b
+
b
c
+
c
d
+
d
a
=
46
ab + bc + cd + da = 46
ab
+
b
c
+
c
d
+
d
a
=
46
. If the minimum possible value of
a
2
+
b
2
+
c
2
+
d
2
a^2 + b^2 + c^2 + d^2
a
2
+
b
2
+
c
2
+
d
2
can be expressed as a rational number
p
q
\frac{p}{q}
q
p
in simplest form, find
p
+
q
p + q
p
+
q
.
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