Question

Розвʼязати рівняння за дискримінантом

Answer 1

$\displaystyle\bf\\25^{x} -26\cdot 5^{x} +25=0\\\\(5^{x})^{2} -26\cdot 5^{x} +25=0\\\\5^{x} =m \ , \ m > 0\\\\m^{2} -26m+25=0\\\\D=(-26)^{2} -4\cdot 25=676-100=576=24^{2} \\\\\\m_{1} =\frac{26-24}{2}=\frac{2}{2} =1\\\\\\m_{2} =\frac{26+24}{2} =\frac{50}{2} =25\\\\1)\\\\m=1\\\\5^{x} =1\\\\5^{x} =5^{0} \\\\\boxed{x=0}\\\\2)\\\\m=25\\\\5^{x} =25\\\\5^{x} =5^{2} \\\\\boxed{x=2}\\\\Otvet \ : \ 0 \ ; \ 2$