Page:Annales de mathématiques pures et appliquées, 1810-1811, Tome 1.djvu/341

329

ÉLIMINATION.

Seconde opération.

Équations $\left\{{\begin{aligned}0=&9y^{8}+16y^{7}+7y^{6}+36y^{5}+35y^{4}-8y^{3}+9y^{2}+4y-12.\\0=&7y^{7}-74y^{6}-90y^{5}+80y^{4}-89y^{3}-54y^{2}+436y+312.\\\end{aligned}}\right.$

${\begin{array}{llll}A=+\,\ 9,&a=+\ \ \ 7,&Ab-Ba=-\ \,778,&a'=+81\cdot \,\ 785,\\B=+16,&b=-\,\ 74,&Ac-Ca=-\ \,859,&b'=+81\cdot \,\ 824,\\C=+\,\ 7,&c=-\,\ 90,&Ad-Da=+\ \,468,&c'=-81\cdot \,\ 678,\\D=+36,&d=+\,\ 80,&Ae-Ea=-1046,&d'=+81\cdot \,\ 892,\\E=+35,&d=-\,\ 89,&Af-Fa=-\ \,430,&e'=+81\cdot \,\ 185,\\F=-\,\ 8,&f=-\,\ 54,&Ag-Ga=+3861,&f'=-81\cdot 4428,\\G=+\,\ 9,&g=+436,&Ah-Ha=+2780,&g'=-81\cdot 3004,\\H=+\,\ 4,&h=+312,&Ai\ -I\ \,a=+\ \ \ \ 84~;\\I\ \,=-12~;\end{array}}$

Troisième opération.

Équations $\left\{{\begin{aligned}0=&7y^{7}-74y^{6}-90y^{5}+80y^{4}-89y^{3}-54y^{2}+436y+312,\\0=&785y^{6}+824y^{5}-678y^{4}+892y^{3}+185y^{2}-4428y-3004.\\\end{aligned}}\right.$

${\begin{array}{llll}A=+\ \ \ 7,&a=+\,\ 785,&Ab-Ba\,=+\,\ 63858,&a'=+9408\cdot \,\ 94,\\B=-\,\ 74,&b=+\,\ 824,&Ac-Ca\,=+\,\ 65904,&b'=+9408\cdot 117,\\C=-\,\ 90,&c=-\,\ 678,&Ad-Da=-\,\ 56556,&c'=+9408\cdot 117,\\D=+\,\ 80,&d=+\,\ 892,&Ae-Ea\,=+\,\ 71160,&d'=+9408\cdot 305,\\E=-\,\ 89,&d=+\,\ 185,&Af-Fa\,=+\,\ 11394,&e'=+9408\cdot 257,\\F=-\,\ 54,&f=-4428,&Ag-Ga\,=-363288,&f'=+9408\cdot \,\ 46,\\G=+436,&g=-3004,&Ah-Ha=-244920~;\\H=+312~;\\\end{array}}$

Quatrième opération.

Équations $\left\{{\begin{aligned}0=&785y^{6}+824y^{5}-678y^{4}+892y^{3}+185y^{2}-4428y-3004,\\0=&94y^{5}+117y^{4}+117y^{3}+305y^{2}+257y+46.\\\end{aligned}}\right.$