ГДЗ по алгебре 9 класс Макарычев Задание 347

\[\boxed{\text{347\ (347).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[\textbf{а)}\ \left( x^{2} + 8x \right)^{2} -\]

\[- 4 \cdot (x + 4)^{2} = 256\]

\[x^{2} + 8x + 116 = (x + 4)^{2} \Longrightarrow\]

\[\Longrightarrow x^{2} + 8x = (x + 4)^{2} - 16.\]

\[Пусть\ \ x^{2} + 8x = a;\ \ \]

\[(x + 4)^{2} = a + 16:\]

\[\ a^{2} - 4 \cdot (a + 16) = 256\]

\[a^{2} - 4a - 64 - 256 = 0\]

\[a^{2} - 4a - 320 = 0\]

\[D_{1} = 2^{2} + 320 = 324\]

\[a_{1} = 2 + 18 = 20;\ \]

\[\ a_{2} = 2 - 18 = - 16.\]

\[1)\ x^{2} + 8x = 20\]

\[x^{2} + 8x - 20 = 0\]

\[D_{1} = 16 + 20 = 36\]

\[x_{1} = - 4 + 6 = 2;\ \]

\[\ x_{2} = - 4 - 6 = - 10.\]

\[2)\ x^{2} + 8x = - 16\]

\[x^{2} + 8x + 16 = 0\]

\[(x + 4)^{2} = 0\]

\[x + 4 = 0\]

\[x_{3} = - 4.\]

\[Ответ:x = - 10;x = - 4;x = 2.\]

\[\textbf{б)}\ 2 \cdot \left( x^{2} - 6x \right)^{2} -\]

\[- 120 \cdot (x - 3)^{2} = 8;\]

\[Пусть\ \ x^{2} - 6x = a;\ \ (x - 3)^{2} =\]

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

\[2a^{2} - 120 \cdot (a + 9) = 8\ \ \ \ \ \ |\ :2\]

\[a^{2} - 60 \cdot (a + 9) - 4 = 0\]

\[a^{2} - 60a - 544 = 0\]

\[D_{1} = 30^{2} + 544 = 1444\]

\[a_{1} = 30 + 38 = 68;\ \ \]

\[a_{2} = 30 - 38 = - 8.\]

\[1)\ x^{2} - 6x = 68\]

\[x^{2} - 6x - 68 = 0\]

\[D_{1} = 9 + 68 = 77\]

\[x_{1,2} = 3 \pm \sqrt{77};\]

\[2)\ x^{2} - 6x = - 8\]

\[x^{2} - 6x + 8 = 0\]

\[D_{1} = 9 - 8 = 1\]

\[x_{1} = 3 + 1 = 4;\ \ x_{2} = 3 - 1 = 2.\]

\[Ответ:\ \ x = 2;x = 4;\]

\[x = 3 - \sqrt{77};x = 3 + \sqrt{77}\text{.\ }\]