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Mathematics
Problem
Find all triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
such that all three of the following equations are satisfied:
a
(
b
+
c
−
5
)
=
7
,
a(b + c - 5) = 7,
a
(
b
+
c
−
5
)
=
7
,
b
(
a
+
c
−
5
)
=
7
,
b(a + c - 5) = 7,
b
(
a
+
c
−
5
)
=
7
,
a
2
+
b
2
=
50.
a^2 + b^2 = 50.
a
2
+
b
2
=
50.
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