Страница 39 номер 165, ГДЗ по алгебре за 9 класс к учебнику Мерзляка

1) \(6x - 5x^{2} = 0\)
\(5x^{2} - 6x = 0\)
\(x(5x - 6) = 0\)
\(x = 0\) или \(5x = 6 \Rightarrow x = 0\) или \(x = 1{,}2\)

2) \(25x^{2} = 81\)
\(25x^{2} - 81 = 0\)
\((5x - 9)(5x + 9) = 0\)
\(5x - 9 = 0\) или \(5x + 9 = 0 \Rightarrow x = \frac{9}{5}\) или \(x = - \frac{9}{5} \Rightarrow x = 1{,}8\) или \(x = - 1{,}8\)

3) \(4x^{2} - 7x - 2 = 0\)
\(D = 49 + 4 \cdot 4 \cdot 2 = 49 + 32 = 81 = 9^{2}\)
\(x_{1} = \dfrac{7 + 9}{8} = \dfrac{16}{8} = 2\)
\(x_{2} = \dfrac{7 - 9}{8} = - \dfrac{2}{8} = - 0{,}25\)

4) \(3x^{2} + 8x - 3 = 0\)
\(\dfrac{D}{4} = 4^{2} + 3 \cdot 3 = 16 + 9 = 25 = 5^{2}\)
\(x_{1} = \dfrac{- 4 + 5}{3} = \dfrac{1}{3}\)
\(x_{2} = \dfrac{- 4 - 5}{3} = - 3\)

5) \(x^{2} + x - 12 = 0\)
\((x - 3)(x + 4) = 0\)
\(x_{1} = 3;\ x_{2} = - 4\)

6) \(2x^{2} + 6x + 7 = 0\)
\(\dfrac{D}{4} = 9 - 14 < 0\)

При отрицательном дискриминанте нет корней

Ответ: 1) \(x_{1} = 0;\ x_{2} = 1{,}2\); 2) \(x_{1} = 1{,}8;\ x_{2} = - 1{,}8\); 3) \(x_{1} = 2;\ x_{2} = - 0{,}25\); 4) \(x_{1} = \frac{1}{3};\ x_{2} = - 3\); 5) \(x_{1} = 3;\ x_{2} = - 4\); 6) нет корней.