Question

$( frac{1}{25} )^{x} -6*( frac{1}{5} ) ^{x} +5=0$

Answer 1

$displaystyle ( frac{1}{25})^{x}-6( frac{1}{5})^{x}+5=0 \ \ ( frac{1}{5})^{2x}-6( frac{1}{5})^{x}+5=0 \ \ ( frac{1}{5})^{x}=a \ \ a^{2}-6a+5+0 \ D=b^{2}-4ac=36-20=16 \ \ a_{1,2}= frac{-bб sqrt{D}}{2a} \ \ a_{1}=5 \ a_{2}=1 \ \ ( frac{1}{5})^{x}=5 \ \ x=-1 \ \ ( frac{1}{5})^{x}=1 \ \ x=0$
Ответ: {-1; 0}