Question

Подробно пожалуйста)

Answer 1

Решено $\checkmark$

С учетом ОДЗ:

x∈[0; 1)U(1; 9]

Answer 2

$\frac{1-x}{1-\sqrt{x}}\geq x-5\; ,\; \; ODZ:\; \; 1-\sqrt{x}\ne 0\; ,\; \; x\ne 1\; ;\; x\geq 0\\\\\frac{(1-\sqrt{x})(1+\sqrt{x})}{1-\sqrt{x}}\geq x-5\\\\1+\sqrt{x}\geq x-5\\\\t=\sqrt{x}\geq 0\; ,\; \; 1+t\geq t^2-5\\\\t^2-t-6\leq 0\; ,\; \; t_1=-2\; ,\; \; t_2=3\\\\(x-3)(t+2)\leq 0\\\\+++(-2)---(3)+++\\\\t\in [-2,3]\\\\\left \{ {{t\in [-2,3]} \atop {t\geq 0}} \right. \; \; \to \; \; t\in [\, 0,3]\; \; \Rightarrow \\\\\left \{ {{\sqrt{x}\geq 0\; ,\; x\ne 1} \atop {\sqrt{x}\leq 3}} \right. \; \; \left \{ {{x\geq 0\; ,\; x\ne 1} \atop {x\leq 9}} \right. \\\\x\in [\, 0,1)\cup (1,9\, ]$