Решебник по алгебре 8 класс Мерзляк ФГОС Задание 655

 

\[\boxed{\mathbf{655\ (655).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\frac{0,25 + 1000}{2} = 500,125\]

\[\frac{2}{\frac{1}{0,25} + \frac{1}{1000}} = 0,5\]

\[2)\ \frac{a + b}{2} = 1,25\]

\[\frac{2}{\frac{1}{a} + \frac{1}{b}} = \frac{2}{\frac{a + b}{\text{ab}}} = \frac{2ab}{a + b} = 250\]

\[\frac{5a - 2a^{2}}{2,5} = 250\]

\[5a - 2a^{2} = 625\]

\[- 2a^{2} + 5a - 625 = 0\]

\[2a^{2} - 5a + 625 = 0\]

\[2 \cdot {0,25}^{2} - 5 \cdot 0,25 + 625 \neq 0\]

\[623,75 \neq 0\]

\[Ответ:нельзя.\]

\[\boxed{\mathbf{6}\mathbf{5}\mathbf{5}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ 6x(3 - x) = 7 - 2x²\]

\[18x - 6x^{2} - 7 + 2x^{2} = 0\]

\[- 4x^{2} + 18x - 7 = 0\]

\[a = - 4,\ \ b = 18,\ \ c = - 7\]

\[2)\ x(x + 1) = (x - 3)(7x + 2)\]

\[x^{2} + x = 7x^{2} + 2x - 21x - 6\]

\[x^{2} + x - 7x^{2} - 2x + 21x + 6 =\]

\[= 0\]

\[- 6x^{2} + 20x + 6 = 0\ \ \ \ \ |\ :( - 2)\]

\[3x^{2} - 10x - 3 = 0\]

\[a = 3,\ \ b = - 10,\ \ c = - 3\]

\[3)\ (5x - 1)^{2} = (x + 4)(x - 2)\]

\[25x^{2} - 10x + 1 = x^{2} + 2x - 8\]

\[25x^{2} - 10x + 1 - x^{2} - 2x + 8 =\]

\[= 0\]

\[24x^{2} - 12x + 9 = 0\ \ \ \ \ |\ :3\]

\[8x^{2} - 4x + 3 = 0\]

\[a = 8,\ \ b = - 4,\ \ c = 3\]

\[4)\ 4x(x + 8) - (x - 6)(x + 6) =\]

\[= 0\]

\[4x^{2} + 32x - x^{2} + 36 = 0\]

\[3x^{2} + 32x + 36 = 0\]

\[a = 3,\ \ b = 32,\ \ c = 36.\]