0 \\ ODZ: 25^{x}-10*5^x+26 \neq 0 \\ \\ 5^{2x}-10*5^x+24+\frac{1}{5^{2x}-10*5^x+26}>0 \\ \\ \\ Pust' 5^{2x}-10*5^x=z , togda: \\ z+24 +\frac{1}{z+26}>0 \\ \frac{z^2+50z+625}{z+26}>0 \\ \\ \frac{(z+25)^2}{z+26}>0 \\ T.k (z+25)^2 \geq 0 \ pri\ lubom \ z \to z+26>0 \\T.k \ z=5^{2x}-10*5^x \to 5^{2x}-10*5^x+26>0 \\5^{2x}-10*5^x+26=0 \\Pust' 5^x=t ,\ to \ 5^{2x}=t^2 \\t^2-10t+26=0 " alt="25^{x}-10*5^{x}+24+ \frac{1}{25^{x}-10*5^x+26}>0 \\ ODZ: 25^{x}-10*5^x+26 \neq 0 \\ \\ 5^{2x}-10*5^x+24+\frac{1}{5^{2x}-10*5^x+26}>0 \\ \\ \\ Pust' 5^{2x}-10*5^x=z , togda: \\ z+24 +\frac{1}{z+26}>0 \\ \frac{z^2+50z+625}{z+26}>0 \\ \\ \frac{(z+25)^2}{z+26}>0 \\ T.k (z+25)^2 \geq 0 \ pri\ lubom \ z \to z+26>0 \\T.k \ z=5^{2x}-10*5^x \to 5^{2x}-10*5^x+26>0 \\5^{2x}-10*5^x+26=0 \\Pust' 5^x=t ,\ to \ 5^{2x}=t^2 \\t^2-10t+26=0 " align="absmiddle" class="latex-formula">
0 \ pri \ lubom \ t \\5^x \ prinimaet \ polojitel'noe \ znachenie\ pri\ lubom\ x \\Otvet:x\mathcal{2}(-\mathcal{1};+\mathcal{1})" alt="\\k=-5, \ D=25-26=-1<0 \to \varnothing \to t^2-10t+26>0 \ pri \ lubom \ t \\5^x \ prinimaet \ polojitel'noe \ znachenie\ pri\ lubom\ x \\Otvet:x\mathcal{2}(-\mathcal{1};+\mathcal{1})" align="absmiddle" class="latex-formula">