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МатематикаРешебник по алгебре 9 класс Макарычев Задание 306
Задание 306
\[\boxed{\text{306\ (306).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ 2x^{2} + 13x - 7 > 0\]
\[2x^{2} + 13x - 7 = 0\]
\[D = 169 + 4 \cdot 2 \cdot 7 = 225\]
\[x = \frac{- 13 \pm 15}{4} = 0,5; - 7;\]
\[2 \cdot (x - 0,5)(x + 7) > 0\]
\[x \in ( - \infty;\ - 7) \cup (0,5; + \infty).\]
\[\textbf{б)} - 9x^{2} + 12x - 4 < 0\ |\ :( - 1)\]
\[9x^{2} - 12x + 4 > 0\]
\[9x^{2} - 12x + 4 = 0\ \]
\[(3x - 2)^{2} > 0\]
\[9 \cdot \left( x - \frac{2}{3} \right)^{2} > 0\]
\[x \in \left( - \infty;\frac{2}{3} \right) \cup \left( \frac{2}{3}; + \infty \right).\]
\[\textbf{в)}\ 6x^{2} - 13x + 5 \leq 0\]
\[6x^{2} - 13x + 5 = 0\]
\[D = 169 - 4 \cdot 6 \cdot 5 = 49\]
\[x_{1,2} = \frac{13 \pm 7}{12} = 0,5;1\frac{2}{3};\ \]
\[6 \cdot (x - 0,5)\left( x - 1\frac{2}{3} \right) \leq 0\]
\[x \in \left\lbrack 0,5;1\frac{2}{3} \right\rbrack.\]
\[\textbf{г)} - 2x^{2} - 5x + 18 \leq 0\ |\ :( - 1)\]
\[2x^{2} + 5x - 18 \geq 0\]
\[D = 25 + 4 \cdot 2 \cdot 18 = 169\]
\[x_{1,2} = \frac{- 5 \pm 13}{4} = 2;\ - 4,5;\]
\[2 \cdot (x - 2)(x + 4,5) \geq 0\]
\[x \in ( - \infty; - 4,5\rbrack \cup \lbrack 2; + \infty).\]
\[\textbf{д)}\ 3x^{2} - 2x > 0\]
\[3x\left( x - \frac{2}{3} \right) > 0\]
\[x \in ( - \infty;0) \cup \left( \frac{2}{3}; + \infty \right).\]
\[\textbf{е)}\ 8 - x^{2} < 0\ \ \ \ \ |\ :( - 1)\]
\[x^{2} - 8 > 0\ \]
\[\left( x - 2\sqrt{2} \right)\left( x + 2\sqrt{2} \right) > 0\]
\[x \in \left( - \infty; - 2\sqrt{2} \right) \cup \left( 2\sqrt{2}; + \infty \right).\]
\[\boxed{\text{306.}\text{\ }\text{ОК\ ГДЗ\ -\ домашка\ на\ 5}}\]
\[\textbf{а)}\ 718x^{4} - 717x^{2} - 1 = 0\]
\[x_{1} = 1;\ \ x_{2} = - 1 \Longrightarrow корни\ \]
\[уравнения,\ находятся\ \]
\[методом\ подбора.\]
\[Схема\ Горнера:\]
| \[718\] | \[0\] | \[- 717\] | \[0\] | \[- 1\] | |
|---|---|---|---|---|---|
| \[1\] | \[718\] | \[718\] | \[1\] | \[1\] | \[0\] |
| \[- 1\] | \[718\] | \[0\] | \[1\] | \[0\] | \[0\] |
\[718x^{4} - 717x^{2} - 1 =\]
\[= (x - 1)(x + 1)\left( 718x^{2} + 1 \right)\]
\[718x^{2} + 1 > 0 \Longrightarrow x_{1} = 1;\ \]
\[\ x_{2} = - 1.\]
\[\textbf{б)}\ 206x^{4} - 205x^{2} - 1 = 0\]
\[x_{1} = 1;\ \ x_{2} = - 1 \Longrightarrow корни.\]
\[\Longrightarrow 206x^{4} - 205x^{2} - 1 =\]
\[= (x - 1)(x + 1)\left( 206x^{2} + 1 \right)\]
\[206x^{2} + 1 > 0 \Longrightarrow x_{1} = 1;\ \ \]
\[x_{2} = - 1.\]
\[Ответ:а)\ - 1;1;\ \ \ б) - 1;1.\]
