Page:Annales de mathématiques pures et appliquées, 1818-1819, Tome 9.djvu/390

382

FORMULES

${\begin{aligned}\\L=&{\frac {x^{10}}{12}}-5x^{9}+138x^{8}-{\frac {6050x^{7}}{3}}+{\frac {157773x^{6}}{8}}-128865x^{5}\\&+{\frac {1708465x^{4}}{3}}-1681900x^{3}+3188394x^{2}-3542880x+1814400,\\M=&{\frac {x^{11}}{13}}-{\frac {11x^{10}}{2}}+175x^{9}-3267x^{8}+{\frac {119141x^{7}}{3}}-{\frac {1318779x^{6}}{4}}\\&+{\frac {13339535x^{5}}{7}}-7665955x^{4}+{\frac {105258076x^{3}}{5}}-37729494x^{2}\\&+40181280x-19958400.\end{aligned}}$

15. En chassant les dénominateurs, ces formules deviennent

${\begin{array}{rl}2A&=1.\\6B&=2x-3.\\4C&=x^{2}-4x\\&+4.\\30D&=6x^{3}-45x^{2}\\&+110x-90.\\12E&=2x^{4}-24x^{3}\\&+105x^{2}-200x\\&+144.\\84F&=12x^{5}-210x^{4}\\&+1428x^{3}-4725x^{2}\\&+7672x-5040.\\24G&=3x^{6}-72x^{5}\\&+700x^{4}-3528x^{3}\end{array}}$