ГДЗ по алгебре 9 класс Макарычев Задание 281

\(\boxed{\text{281\ (281).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\)

\[\textbf{а)}\ x^{4} - 47x^{2} - 98\]

\[x^{2} = t:\]

\[t^{2} - 47t - 98 = 0\]

\[t_{1} + t_{2} = 47;\ \ \ t_{1} \cdot t_{2} = - 98\]

\[t_{1} = 49;\ \ \ t_{2} = - 2.\]

\[t^{2} - 47t - 98 =\]

\[= (t + 2)(t - 49) =\]

\[= (t + 2)(t - 49).\]

\[x^{4} - 47x^{2} - 98 =\]

\[= \left( x^{2} + 2 \right)\left( x^{2} - 49 \right) =\]

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

\[\textbf{б)}\ x^{4} - 85x^{2} + 1764\]

\[x^{2} = t:\]

\[t^{2} - 85t + 1764 = 0\]

\[t_{1} + t_{2} = 85;\ \ \ t_{1} \cdot t_{2} = 1764\]

\[t_{1} = 36;\ \ \ t_{2} = 49.\]

\[t^{2} - 85t + 1764 =\]

\[= (t - 36)(t - 49).\]

\[x^{4} - 85x^{2} + 1764 =\]

\[= \left( x^{2} - 36 \right)\left( x^{2} - 49 \right) =\]

\[= (x - 6)(x + 6)(x - 7)(x + 7).\]