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Mathematics
Mathematics
Problem
If
a
,
b
a, b
a
,
b
and
c
c
c
are non-zero real numbers and if the equations
(
a
−
1
)
x
=
y
+
z
(a-1)x = y + z
(
a
−
1
)
x
=
y
+
z
,
(
b
−
1
)
y
=
z
+
x
(b-1)y = z + x
(
b
−
1
)
y
=
z
+
x
,
(
c
−
1
)
z
=
x
+
y
(c-1)z = x + y
(
c
−
1
)
z
=
x
+
y
has a non-trivial solution, then
a
b
+
b
c
+
c
a
ab + bc + ca
ab
+
b
c
+
c
a
equals to a.
a
+
b
+
c
a + b + c
a
+
b
+
c
b.
a
b
c
abc
ab
c
c. 1 d. None of these
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