1\; \; \to \; \; 9x-15 \geq 2+2x\\\\7x \geq 17\; ,\; \ x \geq \frac{17}{7}\; ,\; \; x \geq 2\frac{3}{7}\\\\x\in [\, 2\frac{3}{7}\; ;\; +\infty )" alt="1)\quad y=\sqrt[4]{ \frac{125^{3x-5}}{64^{3x-5}}-(1\frac{9}{16} )^{1+x}}\\\\OOF:\; \; \frac{(5^3)^{3x-5}}{(4^3)^{3x-5}}-(\frac{25}{16})^{1+x} \geq 0\\\\(\frac{5}{4})^{9x-15} \geq (\frac{5}{4})^{2+2x}\\\\\frac{5}{4}>1\; \; \to \; \; 9x-15 \geq 2+2x\\\\7x \geq 17\; ,\; \ x \geq \frac{17}{7}\; ,\; \; x \geq 2\frac{3}{7}\\\\x\in [\, 2\frac{3}{7}\; ;\; +\infty )" align="absmiddle" class="latex-formula">
0\; ,\; \; t^2\cdot \frac{1}{5}+4t-1\ne 0\; \; \to \\\\t^2+20t-5\ne 0\\\\D=420\; ,\; \; t_{1,2}=\frac{-20\pm \sqrt{420}}{2}=-10\pm \sqrt{105}\\\\t_1\approx 0,25\; ;\; \; t_2\approx -20,25<0\\\\5^{x}\ne -10+\sqrt{105}\; \; \to \; \; x\ne log_5(-10+\sqrt{105})\\\\x\in (-\infty ,-10+\sqrt{105})\cup (-10+\sqrt{105},+\infty )" alt="2)\quad y= \frac{x^2-64}{25^{x-0,5}+4\cdot 5^{x}-1} \\\\OOF:\; \; (5^2)^{x-0,5}+4\cdot 5^{x}-1\ne 0\\\\5^{2x-1}+4\cdot 5^{x}-1\ne 0\\\\5^{2x}\cdot 5^{-1}+4\cdot 5^{x}-1\ne 0\\\\t=5^{x}>0\; ,\; \; t^2\cdot \frac{1}{5}+4t-1\ne 0\; \; \to \\\\t^2+20t-5\ne 0\\\\D=420\; ,\; \; t_{1,2}=\frac{-20\pm \sqrt{420}}{2}=-10\pm \sqrt{105}\\\\t_1\approx 0,25\; ;\; \; t_2\approx -20,25<0\\\\5^{x}\ne -10+\sqrt{105}\; \; \to \; \; x\ne log_5(-10+\sqrt{105})\\\\x\in (-\infty ,-10+\sqrt{105})\cup (-10+\sqrt{105},+\infty )" align="absmiddle" class="latex-formula">