If `a , b , c` are distinct real numbers and the system of equations `a x+a^2y+(a^3+1)z=0` `b x+b^2y+(b^3+1)z=0` `c x+c^2y+(c^3+1)=0` has a non-trivial solution, show that `a b c=-1`

Explanation

We have given: `a , b , c`
are distinct real numbers and the system of equations

`a x+a^2y+(a^3+1)z=0`

`b x+b^2y+(b^3+1)z=0`

`c x+c^2y+(c^3+1)=0`

has a non-trivial solution

Then we have to show that `a b c=-1`

Let

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