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
Create a free account to view solution
View Solution FreeMore Math miscellaneous Questions
The value of 21/4, 41/8, 81/6 + ..... ∞ is...dx is equal to...Let L = 2C0 + C2 + ..... + . Cn (where Cr = nCr). If S = , then which of the following is/are incorrect ?...The coefficient of x13 in the expansion of (1 - x)5 (1 + x + x2 + x3)4 is :-...If one of the lines given by $6x^2 - xy + 4cy^2 = 0$ is $3x + 4y = 0$, then $c$ equals...