${x^3}\, + \,\,5{x^2}\, – \,\,7x\,\, – 1\,\, = \,\,0$

$\alpha ,\,\,\beta ,\,\,\gamma \,\, \to \,$ બીજ $ \Rightarrow \,\,\alpha \beta \gamma \,\, = \,\,1$

એવું સમીકરણ કે જેના બીજ $\frac{{\rm{1}}}{\alpha }\,{\rm{,}}\,\,\frac{{\rm{1}}}{\beta }\,{\rm{,}}\,\,\frac{{\rm{1}}}{\gamma }$ હોય,તો

$\frac{{\rm{1}}}{{{{\rm{x}}^{\rm{3}}}}}\,\, + \,\,\frac{5}{{{x^2}}}\,\, – \,\,\frac{7}{x}\,\, – \,\,1\,\, = \,\,0$ થાય છે.

${\rm{ – }}{{\rm{x}}^{\rm{3}}}\, – \,\,7{x^2}\, + \,\,5x\,\, + \,\,1\,\, = \,\,0\,$ 

$ \Rightarrow \,\,\,{x^3}\, + \,\,7{x^2}\, – \,\,5x\, – \,\,1\,\, = \,\,0$

આપણે આમ લખી શકીએ કે

$\alpha \beta ,\,\,\beta \gamma ,\,\,\gamma \alpha $ 

$\frac{{\alpha \beta }}{{\alpha \beta \gamma }}\,\,\,.\,\,\,\frac{{\beta \gamma }}{{\alpha \beta \gamma }}\,\,\,.\,\,\,\frac{{\gamma \alpha }}{{\alpha \beta \gamma }}\,\,\,\,\,\,\,$   ($\,\,\,\,\alpha \beta \gamma \,\, = \,\,1$)

$\frac{1}{\gamma }\,,\,\,\frac{1}{\alpha }\,,\,\,\frac{1}{\beta }$

તેથી, સમીકરણ કે જેના બીજ $\,\alpha \beta \,{\rm{,}}\,\,\beta \gamma \,{\rm{,}}\,\,\gamma \alpha \,\,$

$ \Rightarrow \,\,\frac{1}{\gamma }\,,\,\,\frac{1}{\alpha }\,,\,\,\frac{1}{\beta }\,$ હોય , તો 

${{\rm{x}}^{\rm{3}}}\, + \,\,7{x^2}\, – \,\,5x\,\, – \,\,1\,\, = \,\,0$ થાય છે.