# I challenge you to solve this properly!

Algebra Level 5

$$a,b,c$$ are the cube roots of $$p, (p<0)$$ then for any permissible values of $$x,y,z$$ which is given by

$$\left| \frac { xa+yb+zc }{ xb+yc+za } \right| +({ a }_{ 1 }^{ 2 }-2{ b }_{ 1 }^{ 2 })\omega +([x]+[y]+[z]){ \omega }^{ 2 }=0$$

(where $$\omega$$ is a cube root of unity, $${ a }_{ 1 }$$ is a positive real and $${ b }_{ 1 }$$ is a prime number). Find the value of $$\left[ x+{ a }_{ 1 } \right] +\left[ y+b_{ 1 } \right] +\left[ z \right]$$ where $$[.] denotes GIF$$.

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