Question Number 36154 by SammyKT last updated on 29/May/18
$${Q}.\:\:{If}\:{x}\neq{y}\neq{z}\:\:{and}\:\:\begin{vmatrix}{{x}}&{{x}^{\mathrm{3}} }&{{x}^{\mathrm{4}} −\mathrm{1}}\\{{y}}&{{y}^{\mathrm{3}} }&{{y}^{\mathrm{4}} −\mathrm{1}}\\{{z}\:}&{{z}^{\mathrm{3}} }&{{z}^{\mathrm{4}} −\mathrm{1}}\end{vmatrix}=\mathrm{0} \\ $$$$ \\ $$$${Prove}\:{that}\:\:{xyz}\left({xy}+{yz}+{zx}\right)=\left({x}+{y}+{z}\right) \\ $$$$ \\ $$$${please}\:{help}. \\ $$