Question

Помогите!!!!!! 5^x-1 + 5*(0,2)^x-2=<26

Answer 1

$5^{x-1}+5*0,2^{x-2}=26$
$5^x* frac{1}{5}+5* (frac{1}{5})^x * (frac{1}{5})^{-2} =26$
$frac{1}{5}*5^x+125* frac{1}{5^x}=26$
$5^x=t$
$frac{1}{5}*t+ frac{125}{t}=26$ $/*t$
$frac{1}{5}t^2-26t+125=0$
$D=676-100=576; sqrt{D}=24$
$x_1= frac{26+24}{0,4}=125$
$x_2= frac{26-24}{0,4}=5$
Производим обратную замену:
$5^x=5$
$x_1=1$

$5^x=125$
$5^x=5^3$
$x_2=3$

Ответ: [1;3]