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МатематикаРешебник по алгебре 8 класс Мерзляк ФГОС Задание 705
Задание 705
\[\boxed{\mathbf{705\ (705).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[x^{2} + 5x - 10 = 0\]
\[x_{1} + x_{2} = - \frac{b}{a} = - 5\]
\[Ответ:2) - 5.\]
\[\boxed{\mathbf{705.\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ (x + 7)(x - 8) - (4x + 1)(x - 2) = - 21x\]
\[x^{2} + 7x - 8x - 56 - 4x^{2} - x + 8x + 2 = - 21x\]
\[- 3x^{2} + 6x + 21x - 54 = 0\]
\[- 3x^{2} + 27x - 54 = 0\ \ \ |\ :( - 3)\]
\[x^{2} - 9x + 18 = 0\]
\[x_{1} + x_{2} = 9;\ \ x_{1} \cdot x_{2} = 18\]
\[x_{1} = 6;\ \ \ x_{2} = 3.\]
\[Ответ:3;6.\]
\[2)\ (2x - 1)(2x + 1) - x(1 - x) = 2x(x + 1)\]
\[4x^{2} - 1 - x + x^{2} = 2x^{2} + 2x\]
\[3x^{2} - 3x - 1 = 0\]
\[D = 9 + 12 = 21\]
\[x = \frac{3 \pm \sqrt{21}}{6}.\]
\[Ответ:x = \frac{3 \pm \sqrt{21}}{6}.\]
\[3)\ 2x^{2} + x\sqrt{5} - 15 = 0\]
\[D = 5 + 120 = 125\]
\[x = \frac{- \sqrt{5} + 5\sqrt{5}}{4} = \frac{4\sqrt{5}}{4} = \sqrt{5};\]
\[x_{2} = \frac{- \sqrt{5} - 5\sqrt{5}}{4} =\]
\[= - \frac{6\sqrt{5}}{4} = - \frac{3\sqrt{5}}{2}.\]
\[Ответ:\sqrt{5};\ - \frac{3\sqrt{5}}{2}..\]
\[4)\ x^{2} - x\left( \sqrt{6} - 1 \right) - \sqrt{6} = 0\]
\[D = \left( \sqrt{6} - 1 \right)^{2} + 4\sqrt{6} =\]
\[= 6 - 2\sqrt{6} + 1 + 4\sqrt{6} =\]
\[= 6 + 2\sqrt{6} + 1 = \left( \sqrt{6} + 1 \right)^{2};\]
\[x_{1} = \frac{\sqrt{6} - 1 + \sqrt{6} + 1}{2} =\]
\[= \frac{2\sqrt{6}}{2} = \sqrt{6};\]
\[x_{2} = \frac{\sqrt{6} - 1 - \sqrt{6} - 1}{2} =\]
\[= \frac{- 2}{2} = - 1.\ \]
\[Ответ:\sqrt{6};\ - 1.\]
\[5)\ \frac{x^{2} - 4}{8} - \frac{2x + 3}{3} = - 1\ \ | \cdot 24\]
\[3x^{2} - 12 - 16x - 24 = - 24\]
\[3x^{2} - 16x - 12 = 0\]
\[D_{1} = 64 + 36 = 100\]
\[x_{1} = \frac{8 + 10}{3} = 6;\]
\[x_{2} = \frac{8 - 10}{3} = - \frac{2}{3}.\]
\[Ответ:\ - \frac{2}{3};\ \ 6.\]
\[6)\ \frac{4x^{2} + x}{3} - \frac{x^{2} + 17}{9} = \frac{5x - 1}{6}\ \ | \cdot 18\]
\[24x^{2} + 6x - 2x^{2} - 34 = 15x - 3\]
\[22x^{2} - 9x - 31 = 0\]
\[D = 81 + 2728 = 2809 = 53^{2}\]
\[x_{1} = \frac{9 + 53}{44} = \frac{62}{44} = \frac{31}{22};\]
\[x_{2} = \frac{9 - 53}{44} = - 1.\]
\[Ответ:\ - 1;\ \ \frac{31}{22}.\]
