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2016 LMT
11
2016 LMT Individual #11
2016 LMT Individual #11
Source:
April 10, 2016
Problem Statement
Find all ordered triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of real numbers such that
{
a
+
b
=
c
,
a
2
+
b
2
=
c
2
−
c
−
6
,
a
3
+
b
3
=
c
3
−
2
c
2
−
5
c
.
\begin{cases} a+b=c,\\ a^2+b^2=c^2-c-6,\\ a^3+b^3 = c^3-2c^2-5c. \\ \end{cases}
⎩
⎨
⎧
a
+
b
=
c
,
a
2
+
b
2
=
c
2
−
c
−
6
,
a
3
+
b
3
=
c
3
−
2
c
2
−
5
c
.
Proposed by Evan Fang
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