x,y,znot all zeros and the equationsx+y+z=0,(1+a)x+(2+a)y−8z=0,x−(1+a)y+(2+a)z=0 have non-trivial solution. Then a =

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2+15

3±15

−5±22

answer is D.

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Detailed Solution

The condition for a homogeneous system of equations to have a non-trivial solution is Δ=0⇒1111+a2+a-81-1+a2+a=0⇒a2+10a+17=0⇒a=−5±22

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