номер 243 гдз 8 класс алгебра Муравин Муравин

1) x² = 81 \begin{equation}x=\pm \sqrt{81}    x_{1}=-9    x_{2}=9 \end{equation}
2) x² = 0,25 \begin{equation}x=\pm \sqrt{0,25}    x_{1}=-0,5    x_{2}=0,5 \end{equation}
3) y² = 11 \begin{equation}y=\pm \sqrt{11}   y_{1}=-\sqrt{11}    y_{2}=\sqrt{11} \end{equation}
4) z² = 0,4 \begin{equation}z=\pm \sqrt{0,4}   z_{1}=-\sqrt{0,4}    z_{2}=\sqrt{0,4} \end{equation}
5) 25x² = 16 \begin{equation}x^{2}=\frac{16}{25} \end{equation} \begin{equation}x=\pm \sqrt{\frac{16}{25}}    x_{1}=-\frac{4}{5}    x_{2}=\frac{4}{5} \end{equation}
6) 36y² = 49 \begin{equation}y^{2}=\frac{49}{36} \end{equation} \begin{equation}y=\pm \sqrt{\frac{49}{36}}    y_{1}=-\frac{7}{6}    y_{2}=\frac{7}{6} \end{equation}
7) 0,01z² = 9 \begin{equation}z^{2}=\frac{9}{0,01}=900     z=\pm \sqrt{900} \end{equation} \begin{equation}z_{1}=-30    z_{2}=30 \end{equation}
8) 0,09x² = 25 \begin{equation}x^{2}=\frac{25}{0,09}    x=\pm \sqrt{\frac{25}{0,09}} \end{equation} \begin{equation}x_{1}=-\frac{5}{0,3}    x_{2}=\frac{5}{0,3} \end{equation} \begin{equation}x_{1}=-\frac{50}{3}    x_{2}=\frac{50}{3} \end{equation}
9) (2x - 5)² = 4
2x - 5 = -2
2x = -2 + 5
2x = 3 \begin{equation}x_{1}=\frac{3}{2} \end{equation} \begin{equation}x_{1}=1,5 \end{equation}
или
2x - 5 = 2
2x = 5 + 2
2x = 7 \begin{equation}x_{2}=3,5 \end{equation}
10) (5y + 3)² = 4
5y + 3 = -2
5y = -3 - 2
5y = -5 \begin{equation}y_{1}=-1 \end{equation}
или
5y + 3 = 2
5y = 2 - 3
5y = -1 \begin{equation}y_{2}=-\frac{1}{5} \end{equation}
11) (z² - 5)² = 16
z² - 5 = -4
z² = -4 + 5
z² = 1 \begin{equation}z=\pm 1 \end{equation}
или
z² - 5 = 4
z² = 4 + 5
z² = 9 \begin{equation}z=\pm 3 \end{equation}
Ответ: \begin{equation}z_{1}=-3    z_{2}=-1    z_{3}=1    z_{4}=3 \end{equation}
12) (y² - 4)² = 25
y² - 4 = -5
y² = -5 + 4
y² = -1
нет решений
или
y² - 4 = 5
y² = 5 + 4
y² = 9 \begin{equation}y=\pm 3 \end{equation} \begin{equation}y_{1}=-3    y_{2}=3 \end{equation}