ГДЗ по алгебре 8 класс Макарычев ФГОС Задание 784

\[\boxed{\text{784.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]

\[Воспользуемся\ теоремой\]

\[\ Виета.\]

\[\textbf{а)}\ x = - 7;\ \ x = 2:\ \]

\[(x + 7)(x - 2) = x^{2} - 2x +\]

\[+ 7x - 14 = x^{2} + 5x - 14.\]

\[Трехчлен:\]

\[x^{2} + 5x - 14.\]

\[\textbf{б)}\ x = 3 - \sqrt{2};\ \ x = 3 + \sqrt{2}:\]

\[\left( x - \left( 3 - \sqrt{2} \right) \right)\left( x - \left( 3 + \sqrt{2} \right) \right) =\]

\[= \left( x - 3 + \sqrt{2} \right)\left( x - 3 - \sqrt{2} \right) =\]

\[= \left( (x - 3) + \sqrt{2} \right) \cdot\]

\[\cdot \left( (x - 3) - \sqrt{2} \right) =\]

\[= (x - 3)^{2} - \left( \sqrt{2} \right)^{2} =\]

\[= x^{2} - 6x + 9 - 2 =\]

\[= x^{2} - 6x + 7.\]

\[Трехчлен:\]

\[x^{2} - 6x + 7.\]