3^x+2 + 9^x+1 - 810 = 0lim x/корен3+x - корень3-xx->0

0 \forall y\\3^y = 27=3^3\\y=3\\x=y-1=2" alt="3^{x+2} + 9^{x+1} - 810 = 0\\3*3^{x+1}+3^{2(x+1)}-810=0\\3^{2y}+3*3^y-810=0; (y=x+1)\\(3^y+30)(3^y-27)=0\\3^y+30>0 \forall y\\3^y = 27=3^3\\y=3\\x=y-1=2" align="absmiddle" class="latex-formula">

$lim_{x \to 0}(\frac{x}{\sqrt{3+x}-\sqrt{3-x}})=\lim_{x \to 0}(\frac{x(\sqrt{3+x}+\sqrt{3-x})}{(\sqrt{3+x}-\sqrt{3-x})(\sqrt{3+x}+\sqrt{3-x})})=\\=\lim_{x \to 0}\frac{x(\sqrt{3+x}+\sqrt{3-x})}{2x}=\frac{2\sqrt{3}}{2}=\sqrt{3}$