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МатематикаГДЗ по алгебре 8 класс Макарычев Задание 547
Задание 547
\[\boxed{\text{547\ (547).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
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\[\textbf{а)}\ 5x^{2} - x - 1 = 0\] \[D = 1 + 20 = 21\] \[x_{1,2} = \frac{1 \pm \sqrt{21}}{10} \approx \frac{1 \pm 4,58}{10}\] \[x_{1} = \frac{1 + 4,58}{10} = \frac{5,58}{10} = 0,56;\] \[x_{2} = \frac{1 - 4,58}{10} = - \frac{3,58}{10} = - 0,36.\] |
\[\textbf{б)}\ 2x^{2} + 7x + 4 = 0\] \[D = 49 - 32 = 17\] \[x_{1,2} = \frac{- 7 \pm \sqrt{17}}{4} \approx \frac{- 7 \pm 4,12}{4}\] \[x_{1} = \frac{- 7 + 4,12}{4} = - 0,72;\] \[x_{2} = \frac{- 7 - 4,12}{4} = - 2,78.\] |
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\[\textbf{в)}\ 3 \cdot \left( y^{2} - 2 \right) - y = 0\] \[3y^{2} - 6 - y = 0\] \[3y^{2} - y - 6 = 0\] \[D = 1 + 72 = 73\] \[y_{1,2} = \frac{1 \pm \sqrt{73}}{6} \approx \frac{1 \pm 8,54}{6}\] \[y_{1} = \frac{1 + 8,54}{6} = \frac{9,54}{6} = 1,59\] \[y_{2} = \frac{1 - 8,54}{6} = \frac{- 7,54}{6} = - 1,26\] |
\[\textbf{г)}\ y^{2} + 8(y - 1) = 3\] \[y^{2} + 8y - 8 - 3 = 0\] \[y^{2} + 8y - 11 = 0\] \[D = 64 + 44 = 108\] \[y_{1,2} = \frac{- 8 \pm \sqrt{108}}{2} \approx \frac{- 8 \pm 10,39}{2}\] \[y_{1} = \frac{- 8 + 10,39}{2} = \frac{2,39}{2} = 1,20\] \[y_{2} = \frac{- 8 - 10,39}{2} = \frac{- 18,39}{2} = - 9,20\ \] |
