Question

Алгебра 11 класс. 2 примера 20 баллов ​

Answer 1

Ответ:

$3)\ \ \left\{\begin{array}{l}log_{0,4}(x^2-7)\geq log_{0,4}2}\\5x^2\geq \dfrac{1}{5}\end{array}\right\ \ \left\{\begin{array}{l}x^2-7\leq 2\\x^2-7>0\\x^2\geq \dfrac{1}{25}\end{array}\right\ \ \left\{\begin{array}{l}x^2\leq 9\\(x-\sqrt7)(x+\sqrt7)>0\\(x-\dfrac{1}{5})(x+\dfrac{1}{5})\geq 0\end{array}\right$

$\left\{\begin{array}{l}(x-3)(x+3)\leq 0\\x\in (-\infty ;-\sqrt7)\cup (\sqrt7;+\infty )\\x\in (-\infty ;-0,2\, ]\cup [\, 0,2;+\infty )\end{array}\right\ \ \left\{\begin{array}{l}x\in [-3\, ;\, 3\, ]\\x\in (-\infty ;-\sqrt7)\cup (\sqrt7;+\infty )\\x\in (-\infty ;-0,2\, ]\cup [\, 0,2;+\infty )\end{array}\right$

$x\in [-3\, ;-\sqrt7\, )\cup (\, \sqrt7\, ;\, 3\, ]$

$4)\ \ \left\{\begin{array}{l}6^{log_{1/7}(x+2)}\geq \dfrac{1}{6}\\log_{0,2}3^{x^2-x}\leq 0\end{array}\right\ \ \left\{\begin{array}{l}log_{1/7}(x+2)\geq -1}\\x+2>0\\3^{x^2-x}\geq 1\end{array}\right\ \ \left\{\begin{array}{l}x+2\leq 7\\x>-2\\x^2-x\geq 0\end{array}\right$

$\left\{\begin{array}{l}x\leq 5\\x>-2\\x(x-1)\geq 0\end{array}\right\ \ \left\{\begin{array}{l}x\leq 5\\x>-2\\x\in (-\infty ;0\, ]\cup [\, 1\, ;+\infty )\end{array}\right\ \ \Rightarrow \ \ \ x\in (-2\, ;\, 0\, ]\cup [\, 1\, ;\, 5\, ]$