Questions
If the system of equations,
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a
a+b+c=0
b
a=b=c
c
Either a+b+c=0 ort a=b=c
d
None of these
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Correct option is A
For a non-trivial solution, abcbcacab=0 ⇒(a+b+c)1bc1ca1ab=0⇒(a+b+c)1bc0c−ba−c0a−bb−c=0⇒(a+b+c)×(−a2−b2−c2+ab+bc+ca)=0⇒−12(a+b+c){(a−b)2+(b−c)2+(c−a)2}=0⇒ Either a+b+c=0Or (a−b)2+(b−c)2+(c−a)2=0⇒ Either a+b+c=0Or a−b=0 , b−c=0 and c−a=0 .Similar Questions
If the system of equations
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