2023 · Q20
If x^n − py^n + qz^n is divisible by x² + abyz − bzx − axy, then what is p/a^n − q/b^n equal to?
Elementary MathematicsAlgebra
- A−1
- B0
- C1
- D2
Explanation
x^2+abyz-bzx-axy=(x-ay)(x-bz). Put x=ay: (ay)^n-py^n+qz^n=0 and x=bz: (bz)^n-py^n+qz^n=0; subtracting gives a^n y^n=b^n z^n, whence p/a^n=1+q/b^n, i.e. p/a^n-q/b^n=1. Option (c).