Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 322

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\[x_{1};\ \ x_{2};\ \ x_{3} - корни\ уравнения.\]

\[x^{3} + ax^{2} + bx + c =\]

\[= \left( x - x_{1} \right)\left( x - x_{2} \right)\left( x - x_{3} \right)\]

\[\left( x^{2} - xx_{1} - xx_{2} + x_{1}x_{2} \right)\left( x - x_{3} \right) =\]

\[= x^{3} - x^{2}x_{1} - x^{2}x_{2} + xx_{1}x_{2} -\]

\[- x^{2}x_{3} + xx_{1}x_{2} + xx_{2}x_{3} -\]

\[- x_{1}x_{2}x_{3}\]

\[x^{3} + ax^{2} + bx + c =\]

\[= x^{3} + \underset{- a}{\overset{\left( - x_{1} - x_{2} - x_{3} \right)}{︸}}x^{2} +\]

\[+ \underset{b}{\overset{\left( x_{1}x_{2} + x_{2}x_{3} + x_{1}x_{3} \right)}{︸}}x -\]

\[- \underset{- c}{\overset{x_{1}x_{2}x_{3}}{︸}}.\]

\[Что\ и\ требовалось\ доказать.\]