Math miscellaneousHard
Question
If a, b, c are non-zero real numbers and if the equations (a - 1)x = y + z, (b - 1)y = z + x, (c - 1) z = x + y has a non-trivial solution, then ab + bc + ca is equal to
Options
A.a + b + c
B.abc
C.1
D.None of these
Solution
From the system of equations
d1 = d2 = d3 = 0 ⇒ D1 = D2 = D3 = 0
D =
= 0
⇒ abc - ab - bc - ca = 0
⇒ ab + bc + ca = abc
d1 = d2 = d3 = 0 ⇒ D1 = D2 = D3 = 0
D =
= 0⇒ abc - ab - bc - ca = 0
⇒ ab + bc + ca = abc
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