1.

If `x=c y+b z ,y=a z+c x ,z=x+a y ,w h e r ex ,y ,z`are not allzeros, then find the value of `a^2b^2c^2+2a b cdot`A. 2B. -1C. 0D. 1

Answer» Correct Answer - D
It is given that there are x,y,z not all zero satisfying `x =cy +bz, y=az+cxand z=bx+zy`, So, the system of equations
`x-cy-bz=0`
`cx-y+az=0`
`bx+ay-z=0`
have non-trivial solutions.
`:.{:[(1,-c,-b),(c,-1,a),(b,a,-1)]=0:}`
`rArr 1-a^2-c^2-b^2-2abc=0rArr a^2+b^2+c^2+2abc=1`


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