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If the system of equations $x + y + z = 0, a x + b y + z = 0, b x + y + z = 0$ has a non-trivial solution then

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b2=2b+1

b2=2b−1

b−a=1

b2=2b

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detailed solution

Correct option is B

The condition for a homogeneous system of equations to have a non-trivial solution is Δ=0⇒111ab1b11=0⇒1[b-1]-1[a-b]+1a-b2=0⇒b2=2b-1

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If the system of equations x+y+z=0, ax+by+z=0, bx+y+z=0 has a non-trivial solution then

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Ready to Test Your Skills?

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If the system of equations $x + y + z = 0, a x + b y + z = 0, b x + y + z = 0$ has a non-trivial solution then