Страница 209 номер 708, ГДЗ по алгебре за 9 класс к учебнику Мерзляка

1) \(3x^{2} - 7x + 2 = 3\left( x - \frac{1}{3} \right)(x - 2)\)
\(D = 49 - 4 \cdot 3 \cdot 2 = 49 - 24 = 25\)
\(x_{1} = \dfrac{7 - 5}{6} = \dfrac{2}{6} = \dfrac{1}{3};\ x_{2} = \dfrac{7 + 5}{6} = \dfrac{12}{6} = 2\)
\(\dfrac{3x^{2} - 7x + 2}{2 - 6x} = \dfrac{3\left( x - \frac{1}{3} \right)(x - 2)}{- 6\left( x - \dfrac{1}{3} \right)} = \dfrac{x - 2}{- 2} = \dfrac{2 - x}{2}\)

2) \(10x^{2} - 9x + 2 = 10\left( x - \frac{2}{5} \right)\left( x - \frac{1}{2} \right)\)
\(D = 81 - 4 \cdot 10 \cdot 2 = 1\)
\(x_{1} = \dfrac{9 - 1}{20} = \dfrac{8}{20} = \dfrac{2}{5};\ x_{2} = \dfrac{9 + 1}{20} = \dfrac{10}{20} = \dfrac{1}{2}\)
\(\dfrac{5xy - 5x - 2y + 2}{10x^{2} - 9x + 2} = \dfrac{5x(y - 1) - 2(y - 1)}{10\left( x - \dfrac{2}{5} \right)\left( x - \dfrac{1}{2} \right)} =\)
\(= \dfrac{(5x - 2)(y - 1)}{10\left( x - \dfrac{2}{5} \right)\left( x - \dfrac{1}{2} \right)} = \dfrac{(5x - 2)(y - 1)}{(5x - 2)(2x - 1)} = \dfrac{y - 1}{2x - 1}\)

Ответ: 1) \(\frac{2 - x}{2}\); 2) \(\frac{y - 1}{2x - 1}\).