Question:
If a system of equations
-ax+y+z=0, x-by+z=0, x+y-cz=0 (a,b,c\ne1)
has a non-zero solution, then (1)/(1+a)+(1)/(1+b)+(1)/(1+c) is
If a system of equations
-ax+y+z=0, x-by+z=0, x+y-cz=0 (a,b,c\ne1)
has a non-zero solution, then (1)/(1+a)+(1)/(1+b)+(1)/(1+c) is
Show Hint
For symmetric systems, convert determinant condition into a symmetric identity.
Updated On: Mar 19, 2026
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The Correct Option is B
Solution and Explanation
For a non-zero solution, determinant of coefficients must be zero.
This gives:
a+b+c+2=abc
Using this identity:
(1)/(1+a)+(1)/(1+b)+(1)/(1+c)=1
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