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求方程各實根的近似值,往往先將各級分離而個別地進行,未有同時全部獲得者,有之,自俄羅斯伟大數學家羅巴切夫斯基創立方法始,茲依據於Я.C.貝吉克維奇著“近似計算”略述共法於下: 設已知一代數方程為a_0x~n+a_1x~(n-1)+a_2x~(n-2)+…+a_n-1~x+a_n=0 (1)其中n為自然數,a_0,a_1,a_2,…,a_n為整數,並設其僅有各不相等的實根而為 |x_1|>|x_2|>|x_3|>…>|x_n|。方程(1)也可寫作 (x-x_1)(x-x_2)(x-x_3)…(x-x_n)=0 (2) 現在讓我們來構成一新方程。以-x代原方程中之x,則必恒得a_0x~n-a_1x~(n-1)+a_2x~(n-2)-a_3~(n-3)+…+(-1)~na_n=O (3)其根為-x_1,-x_2,-x_3,…,-x_n,且由此得
The approximate values of the real roots of equations are often separated first and individually, and not all are obtained at the same time. In other words, since the establishment of the method by the great Russian mathematician Robachevsky, it is based on the .Kerzykevich’s “approximate calculation” outlines the common law in the following way: Let the known generation equation be a_0x~n+a_1x~(n-1)+a_2x~(n-2)+...+a_n-1~ x+a_n=0 (1) where n is a natural number, a_0, a_1, a_2, ..., a_n are integers, and it is set to have only unequal real roots and |x_1|>|x_2|>|x_3| >...>|x_n|. Equation (1) can also be written as (x-x_1)(x-x_2)(x-x_3)...(x-x_n)=0 (2) Let us now form a new equation. To use x in the original equation, we must a_0x~n-a_1x~(n-1)+a_2x~(n-2)-a_3~(n-3)+...+(-1)~na_n =O (3) whose root is -x_1, -x_2, -x_3, ..., -x_n, and thus