[latex]( \frac{1}{25} )^{x} -6*( \frac{1}{5} ) ^{x} +5=0[/latex]

[latex]\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 [/latex] Ответ: {-1; 0}