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Given that the system of equations x=cy...

Given that the system of equations x=cy+bz,y=az+cx,z=bx+ay has non-zero solutions and atleast one of a,b,c is a proper fraction.
The system has solution ,such that-

A

`x:y:z-=(1-2a^2):(1-2b^2):(1-2c^2)`

B

`x:y:z-=1/(1-2a^2):1/(1-2b^2):1/(1-2c^2)`

C

`x:y:z-=a/(1-a^2):b/(1-b^2):c/(1-c^2)`

D

`x:y:z-=sqrt(1-a^2):sqrt(1-b^2):sqrt(1-c^2)`

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