Question

1/5^х-1 - 1/5^х+1=4,8
Как такое решить? Можно с объяснениями

Answer 1

$( frac{1}{5})^{x-1} -( frac{1}{5})^{x+1} =4,8\\ (frac{1}{5})^{x}cdot ( frac{1}{5})^{-1}-( frac{1}{5} )^{x}cdot frac{1}{5}=frac{48}{10} \\ (frac{1}{5})^{x} cdot 5-( frac{1}{5})^{x}cdot frac{1}{5} = frac{24}{5} \\( frac{1}{5})^{x}cdot (5- frac{1}{5})=frac{24}{5} \\(frac{1}{5})^{x}cdot frac{24}{5}= frac{24}{5} \\( frac{1}{5} )^{x}=1\\( frac{1}{5} )^{x}= (frac{1}{5})^{0}\\x=0$