![1.\;\;9^{5x}-9^{5x-1}=8\\ 9^{5x}-9^{5x}\cdot9^{-1}=8\\ 9^{5x}-\frac19\cdot9^{5x}=8\\ \frac89\cdot9^{5x}=8\\ 8\cdot9^{-1}\cdot9^{5x}=8\\ 8\cdot9^{5x-1}=8\\ 9^{5x-1}=1\\ 9^{5x-1}=9^0\\ 5x-1=0\\ 5x=1\\ x=\frac15 1.\;\;9^{5x}-9^{5x-1}=8\\ 9^{5x}-9^{5x}\cdot9^{-1}=8\\ 9^{5x}-\frac19\cdot9^{5x}=8\\ \frac89\cdot9^{5x}=8\\ 8\cdot9^{-1}\cdot9^{5x}=8\\ 8\cdot9^{5x-1}=8\\ 9^{5x-1}=1\\ 9^{5x-1}=9^0\\ 5x-1=0\\ 5x=1\\ x=\frac15](https://tex.z-dn.net/?f=1.%5C%3B%5C%3B9%5E%7B5x%7D-9%5E%7B5x-1%7D%3D8%5C%5C+9%5E%7B5x%7D-9%5E%7B5x%7D%5Ccdot9%5E%7B-1%7D%3D8%5C%5C+9%5E%7B5x%7D-%5Cfrac19%5Ccdot9%5E%7B5x%7D%3D8%5C%5C+%5Cfrac89%5Ccdot9%5E%7B5x%7D%3D8%5C%5C+8%5Ccdot9%5E%7B-1%7D%5Ccdot9%5E%7B5x%7D%3D8%5C%5C+8%5Ccdot9%5E%7B5x-1%7D%3D8%5C%5C+9%5E%7B5x-1%7D%3D1%5C%5C+9%5E%7B5x-1%7D%3D9%5E0%5C%5C+5x-1%3D0%5C%5C+5x%3D1%5C%5C+x%3D%5Cfrac15)
1\;-\;HE\;\;nogx.\\ \sin x=1\\ x=\frac\pi2+2\pi n,\;\;n\in\mathbb{Z}" alt="2.\;\;2\cos^2x-\sin x+1=0\\ 2-2\sin^2x-\sin x+1=0\\ 2\sin^2x+\sin x-3=0\\ \sin x=t,\;\;\sin^2x=t^2,\;\;t\in[-1;1]\\ 2t^2+t-3=0\\ D=1-4\cdot2\cdot(-3)=1+24=25\\ t_1=1\\ t_2=-\frac64>1\;-\;HE\;\;nogx.\\ \sin x=1\\ x=\frac\pi2+2\pi n,\;\;n\in\mathbb{Z}" align="absmiddle" class="latex-formula">
Исследование лень писать))