Страница 210 номер 622, ГДЗ по алгебре за 9 класс к учебнику Алимова с ответами и решением

1) \(x^{4} - 17x^{2} + 16 = 0\)
\(x^{2} = z\)
\(z^{2} - 17z + 16 = 0,\)
\(z_{1{,}2} = \dfrac{17 \pm \sqrt{289 - 64}}{2},\)
\(z_{1} = 1, z_{2} = 16;\)
\(x_{1{,}2} = \pm 1, x_{3{,}4} = \pm 4;\)

2) \(x^{4} - 37x^{2} + 36 = 0\)
\(x^{2} = z\)
\(z^{2} - 37z + 36 = 0,\)
\(z_{1{,}2} = \dfrac{37 \pm \sqrt{1369 - 144}}{2},\)
\(z_{1} = 1, z_{2} = 36\)
\(x_{1{,}2} = \pm 1, x_{3{,}4} = \pm 6;\)

3) \(2x^{4} - 5x^{2} - 12 = 0\)
\(x^{2} = z\)
\(2z^{2} - 5z - 12 = 0,\)
\(z_{1{,}2} = \dfrac{5 \pm \sqrt{25 + 96}}{4},\)
\(z_{1} = 4, z_{2} = -\dfrac{3}{2}\)
\(x_{1{,}2} = \pm 2;\)
\(x^{2} = -\dfrac{3}{2}, x_{3{,}4} = \pm i\sqrt{\dfrac{3}{2}} = \pm\dfrac{i\sqrt{6}}{2};\)

4) \(x^{4} - 3x^{2} - 4 = 0\)
\(x^{2} = z\)
\(z^{2} - 3z - 4 = 0,\)
\(z_{1{,}2} = \dfrac{3 \pm \sqrt{9 + 16}}{2},\)
\(z_{1} = 4, z_{2} = -1\)
\(x_{1{,}2} = \pm 2;\)
\(x^{2} = -1, x_{3{,}4} = \pm i.\)