If a system of equation \[-ax+y+z=0\] |
\[x-by+z=0\] |
\[x+y-cz=0\]\[(a,b,c\ne -1)\] |
has a non-zero solution then \[\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}=\] |
A) \[0\]
B) \[1\]
C) \[2\]
D) \[3\]
Correct Answer: B
Solution :
for non-zero solution |
\[\Rightarrow \,abc-a-b-c-2=0\] |
\[\Rightarrow \,abc=a+b+c+2\] |
Now, \[\frac{1}{1+a}+\frac{1}{1+b}+\frac{1}{1+c}\]\[=\frac{3+2(a+b+c)+(ab+bc+ac)}{1+(a+b+c)+(ab+bc+ac)+abc}\] |
\[=\frac{3+2(a+b+c)+(ab+bc+ac)}{1+2(a+b+c)+2+ab+bc+ac}=1\] |
You need to login to perform this action.
You will be redirected in
3 sec