যদি \(\left|\begin{array}{lll} x^{\mathbf{k}} & x^{\mathbf{k}+2} & x^{k+3} \\ \mathbf{y}^{\mathbf{k}} & \mathbf{y}^{\mathbf{k}+2} & \mathbf{y}^{\mathbf{k}+3} \\ z^{\mathbf{k}} & z^{\mathbf{k}+2} & z^{\mathbf{k}+3} \end{array}\right|\) \(=(x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)\) হয়, তাহলে